Determination of the viscosity of the cytoplasm of M-HeLa cells using fluorescent magnetic nanoparticles and an electromagnetic needle

doi:10.21203/rs.3.rs-1994074/v1

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Determination of the viscosity of the cytoplasm of M-HeLa cells using fluorescent magnetic nanoparticles and an electromagnetic needle

https://doi.org/10.21203/rs.3.rs-1994074/v1

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Magnetic nanoparticles (MNPs) have recently begun to be actively used in biomedicine as magnetic biosensors for targeted drug delivery in tissue engineering, and in magnetic resonance imaging. The study of the magnetic field effect on magnetic nanoparticles internalized into cells is of particular importance since it allows a non-invasive influence on cellular activity. There is data stating the possibility to manipulate and control individual MNPs by utilizing the local magnetic field gradient created with the help of electromagnetic needles (EN). The measuring of the movement rate of MNPs inside cells under the action of a known magnetic force allows to evaluate the viscous properties of the cell’s cytoplasm. The present work demonstrates the influence of the local magnetic field gradient created by EN on the luminescent MNPs internalized in HeLa cancer cells. It describes a method for controlling the intensity of this field and estimates the attractive force of EN. Both designs of EN and its main characteristics are also described. The applicability of the developed method in measuring the viscosity of the HeLa cancer cells cytoplasm is highlighted.

Electromagnetic Needle

Ferromagnetic Nanoparticles

HeLa Cells

Viscosity

Non-invasive action on the cells and tissues of the body is currently one of the promising areas of research in biology and medicine (Dobson et al. 2006; Ito et al. 2005; Maier-Hauff et al. 2011). Finding of ways to exert a controlled influence on cell activity is an important problem in nanotechnology and nanomedicine (Jung et al. 2014; Schöneborn et al. 2019). Particularly promising are the studies related to the development and study of ferromagnetic nanoparticles, the properties of which can be controlled at a distance using magnetic fields (Kunze et al. 2015; Polte et al. 2007; Riggio et al. 2014). Magnetic nanoparticles (MNPs) have recently begun to be actively used in biomedicine as magnetic biosensors for targeted drug delivery, tissue engineering, and magnetic resonance imaging (Erofeev et al. 2018; Golovin et al. 2017). The magnetic field is non-invasive and can penetrate deeply into living tissues. However, to overcome the weak interaction between magnetic fields and biological tissues, magnetic fields must be converted into mechanical forces, heating, or changes in electrical potential (Dante et al. 2017; Kilinc et al. 2015; Pashut et al. 2014; Shinkai et al. 1996)..Superparamagnetic iron oxide nanoparticles can be considered as a promising tool for such translation mediated by magnetic fields. Due to its deep penetration into living tissues, the magnetic field can noninvasively affect the properties of cells with the internalized MNPs (Long et al. 2015). This effect can be manifested in the form of a thermal effect due to heating induced by a high-intensity alternating magnetic field or the so-called magnetothermia (Deatsch and Evans 2013). Also, the effect on cells can be mediated by mechanical action on cell organelles and membranes during the movement of magnetic nanoparticles when a magnetic field is applied (Dobson 2008; Kilinc et al. 2015). This mechanical actions can lead to the activation of physiological processes that change cellular activity. In particular, this is the activation of ion channels and membrane receptors (Gualdani et al. 2019; Kargol et al. 2015; Nakayama et al. 2015), and the destruction of cell membranes when strong magnetic fields are applied (Golovin et al. 2017; Mustapić et al. 2016). The mechanical movement of the MNPs internalized into the cell cytoplasm under the influence of a magnetic field is used to assess the viscosity properties of the cell’s cytoplasm (Bausch et al. 1999).The viscoelasticity of the cytoplasm is one of the important parameters of cellular processes, such as the transport of vesicles and other intracellular compartments. It is also important for cellular locomotion. The viscoelastic properties of the cytoplasm change at the stage of cell division and can characterize the stages of division (Chen et al. 2014).

Electromagnetic tweezers are used to measure the viscoelastic properties of the cytoplasm and generate an electromagnetic field to influence the MNPs (Bausch et al. 1999). An electromagnetic needle can be considered as one of the modifications of electromagnetic tweezers used for local manipulation of MNPs, which allows the targeted action on individual cells with the internalized MNPs (Cenev et al. 2018; Seon et al. 2020).Using this approach, it was possible to control the cell growth of retinal ganglion cells that were cultured on gold and nickel meshes and in neurons using the membrane-bound MNPs (Pita-Thomas et al. 2015; Ren et al. 2018). This experimental approach made it possible to obtain the directed growth of neurons in the primary culture of the chicken brain. (Fass and Odde 2003). The studies listed above did not control or describe the movement of nanoparticles in a magnetic field inside living cells. In the present study, we used the already reported MNPs with a fluorescent label. Due to the presence of a fluorescent label, it became possible to use confocal microscopy methods, which made it possible to characterize the amount of movement of nanoparticles internalized into HeLa cancer cells in a magnetic field gradient created by an electromagnetic needle. In this study, we also estimated the magnitude of the attraction force of the electromagnetic needle at different magnetic field inductions. Using the proposed approach to measure the movement of magnetic nanoparticles in the cytoplasm, we measured the viscosity of the cell’s cytoplasm using fluorescent magnetic particles and the method of confocal microscopy.

2.1. Magnetic nanoparticles

In the present study, superparamagnetic SPION NPs with an iron oxide core and a fluorescent complex [Ru(dipy)₃]²⁺ are used. The MNP data was synthesized in accordance with the previously published procedure (Fedorenko et al. 2019). These are amino-modified silica nanoparticles (78 nm in diameter) doped with iron oxide cores. The surface exposed amino groups facilitate the cell internalization of the MNPs. The encapsulation of [Ru(dipy)₃]²⁺ phosphorescent complexes into a silica matrix which allows to control the penetration of the MNPs into cells and to monitor the behavior of the MNPs inside cells using a confocal fluorescent microscope due to the bright emission in the red wavelength range upon the excitation (450 nm). The magnetic properties of the MNPs are ensured by the inclusion of superparamagnetic iron oxide cores 17.1 nm in size in the silica matrix (Fedorenko et al. 2019).

2.2. Cells

HeLa cells were obtained from the collection of cell cultures of the Institute of Cytology, Russian Academy of Sciences. The cells were seeded on poly-L-lysine coated cover glasses placed in 6-well plates in DMEM containing 1% L-glutamine, 0.1% gentamicin and 10% FBS. Cells were cultured in a 5% CO2 atmospheric condition at 37°C. Cells were loaded with the MNPs on the third day after seeding for 24 hours. The MNPs were added directly to the culture medium. The final concentration of the MNPs was 20 µg/mL. The internalization of the MNPs into motor neurons was analyzed using a Leica SP5 TCS confocal laser microscope.

2.3. Electromagnetic needle

The EN was fabricated similar to the design described in (Cenev et al. 2018; Seon et al. 2020). A stainless steel rod with a diameter of 4 mm was used as the EN. Using electrolysis in 10% HCl solution, the tip of the rod was reduced (etched) to 40 µm in diameter (Fig. 1a). To generate a magnetic field, the needle was placed in a PLA (polylactide) housing printed on an Anet A6l 3D printer (using the Fusion360 program for modeling), with a copper winding wire with a diameter of 0.2 mm (3300 turns) wound around it (Fig. 1b).

2.4. Calculation of the EN`s force

Calculations to find the attractive force of the EN were carried out experimentally using the mathematical model described in (Cenev et al. 2018; Seon et al. 2020). To do this, the tip of the needle was placed in distilled water with the MNPs added to it at a ratio of 20 µg/mL. Subsequently, the MNPs were attracted to each other in the water, forming conglomerates ~ 1 µm in diameter; all subsequent calculations were performed with microscopic MNP conglomerates. The needle was connected to a B5-44A direct current source, the voltage was applied in the range of 1–6 V with a step of – 1 V. A video of the attraction of microparticles at various voltages of 1–6 V was recorded, which was further divided into frames. Frame rate fps = 3.74625 1/sec, time between frames t = 1/f = 0.2669336 sec. On each frame, the position of the particles was fixed, the distance between the tip of the needle and the particles was found, and the particle sizes were also determined. The movement of the particles was determined by the difference in distance between the particle and the tip of the needle between adjacent frames. The velocities $\vartheta$ for each particle were calculated using formula (1):

$$\vartheta =\frac{\varDelta x}{\varDelta t}$$

where $\varDelta x$ is the movement of the particle, $\varDelta t$ is the time of movement of the particle.

The motion of a particle can be modeled according to the law (2):

$$m\ddot{x}={F}_{Stocks}+{F}_{EN}$$

where $m$ is the mass of the particle, $\ddot{x}$ is the acceleration of the particle, ${F}_{Stocks}$ is the Stokes force, ${F}_{EN }$is the attractive force of the EN.

We can consider the acceleration $\ddot{x}$ = 0 on an infinitely small section and therefore, we obtain Eq. (3):$-{F}_{Stocks}={F}_{EN}. \left(3\right)$

We calculate the force of the needle for each particle according to the formula (4):

$${F}_{EN}=6\pi \bullet \mu \bullet r\bullet \vartheta$$

Where $\mu$ is the viscosity of the liquid in which the particles are located, r is the radius of the particle.

Plots of force versus distance were plotted for particles at voltages of 1–6 V (µ for water was taken as ${10}^{-3}$Pa∙s or ${10}^{-3}$ kg/m∙s). The resulting graphs were approximated similarly to formula (5) described in (Cenev et al. 2018; Seon et al. 2020):

$${ F}_{m}= \frac{2\pi }{3}{d}_{p}^{3}{\rho }_{p}{M}_{p}\frac{\beta {M}_{n}^{2}}{{\left(4\beta \delta +1\right)}^{3}} \left(5\right)$$

Where Fm is the magnetic force depending on the distance between the particle and the needle tip; dp, ${\rho }_{p}$ and ${M}_{p}$are the diameter, density, and mass magnetization of the particle respectively; β is a coefficient related to the pole shape, Mn is the needle core magnetization, δ is the distance between the needle tip and the particle.

This Eq. (5) was rewritten in the form (6), according to which further approximation was carried out:

$$F= \frac{\sigma {d}^{3}\beta }{{\left(4\beta \delta +1\right)}^{3}}, \left(6\right)$$

Where σ is a parameter proportional to the density, mass magnetization of the particle and the needle core magnetization. In our calculations, this parameter was selected for each conglomerate separately in order to approximate the obtained graphs of the dependence of the attracting forces of the EN on the distance.

2.5. Calculation of the cytoplasmic viscosity of HeLa cancer cells

The viscosity of the cytoplasm was calculated using the Stokes formula (7):

$$\mu = \frac{{F}_{EN}}{6\pi \bullet r\bullet \frac{dx}{dt}}, \left(7\right)$$

where µ is the viscosity of the medium in which the MNPs are located, ${F}_{EN}$ is the EN force at a distance of 200 µm between the needle and the particle, r is the particle radius, dx is the displacement of the MNPs inside the cells, and t is the magnetic field stimulation time. According to the microscopic measurements, the radius of the nanoparticle conglomerate was taken as 1 µm, and the magnetic stimulation time was 180 sec (3 minutes).

2.6. Microscopic technique

To calculate the attractive force of the EN, a Nikon Inverted Microscope Eclipse TE300 fluorescent microscope equipped with a fluorescence filter cube, mercury lamp and an AxioCam MRm ZEISS camera was used. AxioVision Rel 4.8. software was used for visualization, the screen video was recorded using the Bandicam 2.3.1.840 program.

Measurements related to the study of the movement of MNPs inside HeLa cancer cells were carried out using a Leica SP5 TCS confocal laser microscope using an argon laser with a wavelength of 488 nm. Nanoparticles were visualized by detecting fluorescence in the range of 600–640 nm. The XYZt confocal microscope mode was used. Leica SP5 TCS orthogonal section instruments were used to determine the position of the maximum fluorescence intensity. To determine changes in MNP localization, we analyzed the position of the maximum fluorescence intensity from a single nanoparticle and its movement along the z axis before and after the application of a magnetic field.

At the first stage of the work, the attractive force of the manufactured EN was calculated according to the method given in the Materials and methods section. For the detailed description of experimental procedure and calculations see the Exp. Section (2.4.). As a result, the average value of the attractive force of the EN for three particles was found for the voltage range of 1–6 V with a step of 1 V, and graphs of the dependencies of the needle attraction force on the distance between the center of the needle and the particle at various voltages were plotted (Fig. 2a), along with the dependence of attracting force of the EN depending on the applied voltage (Fig. 2b).

It was found that with a decrease in the distance between the EN and the particle, as well as with an increase in the applied voltage, the attractive force of the EN increases. The results are listed in Table 1.

In the next series of experiments, using EN, we studied the effect of the magnetic field gradient on MNPs loaded into HeLa cancer cells. Cells in culture were loaded with nanoparticles according to the method described by S. Fedorenko (Fedorenko et al. 2019). As a result, 100 percent of the cells in culture were internalized with MNPs (Fig. 3), which is consistent with the results previously obtained with these nanoparticles on motor neurons (Fedorenko et al. 2019).

Cells internalized with nanoparticles were placed on the object stage of a confocal microscope, and the EN were brought to the cell along with nanoparticles using a micromanipulator under visual control (Fig. 4). The average distance from the EN to the cell was 200 µm. The distance was determined using the confocal microscope software. The lens was focused on the tip of the EN and, using a Z-drive, the cell with MNPs was focused. The Z-drive scale could be used to determine the distance from the needle to the cage. Then the magnetic field was turned on for 180 seconds and video images were recorded in the XYZt mode. The recording was carried out for a voltage range of 1–6 V, for which the force of attraction of the EN was previously calculated (see Fig. 2a). MNPs form conglomerates in cells; observations were made of conglomerates with an average radius of 1 µm. The movement of the MNPs in the cells was detected after the voltage was applied (Fig. 5).

After recording the video, the experimental data were processed and the displacement of the MNP conglomerate was analyzed depending on the magnitude of the applied force. The analysis was performed by shifting the peaks of MNP fluorescence intensity in cancer cells using the Leica SP5 TCS confocal laser microscope software in the absence and presence of a magnetic field generated by the EN at various voltages of 1–6 V with a step of 1 V (Fig. 5). A relationship was also noted between the applied voltage and the displacement of MNP in HeLa cancer cells: as the voltage increased from 1 to 6 V, the displacement itself increased from 1.01 ± 0.03 to 2.03 ± 0.05 µm, respectively. The measurement results are listed in Table 1. The magnetic field induction at the EN tip was assessed using a constructed device based on a Hall sensor (Blokhin et al. 2020), the residual magnetization was removed by applying an alternating magnetic field (Table 1).

Table 1

Relationship between the applied voltage on the coil and the magnetic field induction, displacement of MNP in HeLa cancer cells and the average value of the magnetic force.
Voltage, V	Current, mA	Needle magnetic field induction, mT	Displacement value, µm	The value of the average force (at a distance of 200 µm between the EN and the particle), pN	The value of the average force (at a distance of 20 µm between the EN and the particle), pN
1	29	3.3 ± 0.33	1.01 ± 0.03	0.056 ± 0.002	9.75 ± 1.82
2	59	6.0 ± 0.58	1.13 ± 0.04	0.103 ± 0.017	11.47 ± 2.02
3	86	7.4 ± 0.55	1.23 ± 0.03	0.127 ± 0.019	14.55 ± 2.61
4	116	8.1 ± 0.28	1.41 ± 0.05	0.198 ± 0.033	16.59 ± 2.96
5	144	9.5 ± 0.29	1.7 ± 0.04	0.236 ± 0.05	18.3 ± 2.02
6	169	10.7 ± 0.33	2.03 ± 0.05	0.302 ± 0.027	37.85 ± 3.4

According to the method described in the Exp. Section (1.5), the average viscosity of the cytoplasm of HeLa cancer cells was calculated at a voltage of 6 V. The results are listed in Table 2.

Table 2

Average viscosity of the cytoplasm of HeLa cancer cells, displacement value of the MNP and the average value of the magnetic force at a voltage of 6 V on the coil.
Voltage, V	Displacement value (average), µm	The value of the average force (at a distance of 200 µm), pN	The average viscosity of the cytoplasm of Hela cancer cells, Pa·s
${U}$	${d}{x}$	${{F}}_{{E}{N}}$	${\mu }$
6	2.03 ± 0.05	0.302 ± 0.027	1.45 ± 0.04

As a result of calculations, the average viscosity of the cytoplasm of HeLa cancer cells was 1.45 ± 0.04 Pa·s.

The literature data describe a fairly wide range of viscosities of the cell cytoplasm, which can differ by orders of magnitude. It is known that the viscosity of the cell cytoplasm depends on many parameters, including the density of cell compartments, cytoskeleton, etc. (Xie and Minc 2020). It has been shown that the viscosity properties of the cytoplasm also change depending on the stage of cell development (Chen et al. 2014). In early studies performed using the method of spectrally resolved fluorescence measurements of a porphyrin-dimer-based molecular rotor, the obtained values of the viscosity of the cytoplasm of HeLa cells are in the range of 0.05–0.2 Pa·s (Kuimova et al. 2009; Kuimova et al. 2008). In the work performed on fibroblasts and MDCK cells using rotational magnetic spectroscopy, the obtained viscosity values are also in the range of 0.1-1 Pa·s (Chevry et al. 2013). It should be also noted that the cell viscosity was measured by different methods, which can also affect the results obtained. The work of J.-F. Berret et al. represents the local viscoelasticity of living cells measured by rotational magnetic spectroscopy. Using this method, it was found that the viscosity of the cytoplasm of HeLa cancer cells is in the range of 10–100 Pa·s (Berret 2016). A. Bausch with coauthors in his article determined the viscosity of macrophages, it turned out to be 210 ± 143 Pa·s (Bausch et al. 1999). However, Y. Chen et al. noted in his work noted that the viscosity of fibroblasts, as well as the viscosity of spermatocytes, was 0.26 ± 0.21 Pa·s and 0.04–0.36 Pa·s, respectively (Chen et al. 2014). These parameters were calculated from the Brownian motion of microparticles inside cells at different stages of cell division. These differences are associated with a variety of methods for measuring the viscosity and the state of the cellular cytoplasm. In the present study, we determined the dynamic viscosity of the cell cytoplasm using the classical Stokes formula. The viscosity determination is based on the calculation of the speed of the particles movement inside the cells cytoplasm under the action of a known force. An analysis of the velocity of movement of MNPs in a medium under the action of a known force makes it possible to calculate the viscosity of the medium in which movement occurs (Rodríguez-Rodríguez et al. 2020). In particular, this method can be used to evaluate the viscosity of the cell’s cytoplasm (Bausch et al. 1999). Currently, various methodological approaches are used to measure the viscosity of the cell cytoplasm, including passive microrheology which measures the viscoelasticity of the sample of interest by tracking and analyzing the thermal motion of one or more probes either embedded inside or attached to the sample. The use of such approaches has a number of limitations, since Brownian motion is highly dependent on temperature (Chen et al. 2014). Theoretically, passive microrheology is valid for the determination of cellular viscoelasticity but only if the cell can be regarded as an equilibrium system (Wilhelm 2008). There are also active microrheology methods that imply active influence on test particles in a microsystem and registration of particle responses to this active influence. Such methods include the method of rotational magnetic spectroscopy, but its implementation requires the synthesis of special microwires and it requires the imposition of a field of a certain frequency and complex measurements and calculations (Berret 2016). There are methods using magnetic nanoparticles and magnetic tweezers (Bausch et al. 1999) they are based on the fact that a force of known magnitude, generated by a magnetic field, is applied to magnetic particles internalized into cells. Then, the trajectory and speed of movement of the particles are recorded and these parameters are used to calculate the viscosity. It is well-known that the movement of magnetic nanoparticles was recorded using light microscopes and conventional video cameras (Bausch et al. 1999; Cenev et al. 2018; Seon et al. 2020). In the present study we used a similar approach, but unlike previous works, we used new fluorescent magnetic nanoparticles that can be used in fluorescence confocal microscopy. The use of the confocal microscopy technique using fluorescent magnetic nanoparticles makes it possible to conduct studies in three dimensions and with a higher resolution than in conventional optical microscopy. The presence of a fluorescent label in nanoparticles allows the use of microparticles of smaller diameter, which have a better penetrating ability into cells. The particles used in our studies penetrated 100 percent of the cells (Fedorenko et al. 2019). Due to the presence of the label ([Ru(dipy)3]2+), they can be easily detected in cells. Previous studies have used a ballistic method to load cells with microparticles, which requires the special equipment (Chen et al. 2014).

In this paper, we present a highly deterministic manipulation technique with magnetic nanoparticles inside cells. We characterized and calculated the distance of movement of magnetic nanoparticles inside cells under the action of a local magnetic field gradient caused by EN. Due to the obtained experimental data and calculations, it was possible to calculate the force with which the magnetic field acts on MNPs and calculate the viscosity of the medium in which the nanoparticles move. The viscosity values obtained are in good agreement with the data obtained by other methods. Thus, the proposed method can be used to measure the viscosity of the cytoplasm of different cells under different physiological conditions. The attractive force of MNPs created by an electromagnetic needle at various voltages from 1 to 6 V was measured. A relationship was noted between the applied voltage and the displacement of MNPs in cells: with an increase in voltage from 1 to 6 V, the displacement itself increased from 1.01 ± 0.03 to 2.03 ± 0.05 µm respectively. The magnitude of the attractive force that we obtained (at a voltage of 1–6 V) amounted from 0.056 ± 0.002–0.302 ± 0.027 pN (at a distance of 200 µm between the EN and the particle) to 9.75 ± 1.82–37.85 ± 3.4 pN (at a distance of 20 µm between the EN and the particle) fits into the range of forces that were described and used by other authors in their works (Golovin et al. 2017; Pita-Thomas et al. 2015). They showed that particles, when exposed to magnetic forces of similar orders, are able to cause activation of ion channels and receptors on the membrane. At the same time, due to the influence of the magnetic field on MNPs located on the filopodia membrane of the axon growth cone of retinal ganglion cells, it is possible to control the direction of filopodia growth (Pita-Thomas et al. 2015).

Thus, the described method makes it possible to manipulate nanoparticles locally inside individual cells and allows for dosed mechanical action on cell membranes and organelles. Using this approach, it was possible to determine the viscosity of the cell cytoplasm. This method will allow mechanical action on cell membranes and potentially trigger cell signaling. Mechanical action on cell membranes in excitable cells can promote the activation of mechano-sensitive channels and, as a result, promote the entry of calcium (Soloperto et al. 2018). Which, in turn, can lead to the launch of various intracellular signal chains (Berridge 1993; Steketee et al. 2011). In the works presented earlier, such an impact was performed using a constant magnetic field, which cannot be quickly dosed and select individual cells for exposure (Tay et al. 2016). Using EN, it is possible to dose and locally create a magnetic field gradient and act on individual cells or on sections of the membrane of individual cells. For example, it is possible to trigger signaling processes locally in individual nerve cells (Gonnissen et al. 2016) or even in individual dendrites (Kilinc et al. 2015; Riggio et al. 2014). Using the effect of the local gradient of the EN magnetic field on MNPs internalized into cells can serve as a powerful tool for studying signaling processes in living cells.

Author contributions All authors contributed equally to this work. D. V. S. and K. A. P. developed the concept and designed experiments, wrote the paper. D. V.S., I. F. R., and G. V. S. performed the experiments; M. A. S. contributed to the electromagnetic needle fabrication. S.V.F. and A.R.M. developed and synthesized nanoparticles. D. V. S. supervised the project. All authors discussed the results and implications and commented on the manuscript at all stages.

Acknowledgements. Authors would like to acknowledge the Federal Research Center "Kazan Scientific Center of RAS" for the provided equipment for the fluorescence research and Kazan National Research Technical University named after A.N. Tupolev for the provided equipment for the cell cultures.

Funding The research was supported by the Russian Science Foundation (project. No. 22-25-00731).

Conflicts of interest. The authors declare no conflict of interest. Consent for publication. All authors gave consent for the publication of the final manuscript.

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Determination of the viscosity of the cytoplasm of M-HeLa cells using fluorescent magnetic nanoparticles and an electromagnetic needle

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Abstract

Figures

1. Introduction

2. Materials And Methods

2.1. Magnetic nanoparticles

2.2. Cells

2.3. Electromagnetic needle

2.4. Calculation of the EN`s force

2.5. Calculation of the cytoplasmic viscosity of HeLa cancer cells

2.6. Microscopic technique

3. Results And Discussion

4. Conclusion

Declarations

References

Additional Declarations

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Voltage, V	Displacement value (average), µm	The value of the average force (at a distance of 200 µm), pN	The average viscosity of the cytoplasm of Hela cancer cells, Pa·s
\({U}\)	\({d}{x}\)	\({{F}}_{{E}{N}}\)	\({\mu }\)
6	2.03 ± 0.05	0.302 ± 0.027	1.45 ± 0.04