The authors would like to acknowledge all the members of CENABIO advanced microscopy facility for all-important help. This work was supported by the Brazilian agencies Conselho Nacional de Desenvolvimento Cient&#237;fico e Tecnol&#243;gico (CNPq), Coordena&#231;&#227;o de Aperfei&#231;oamento de Pessoal de N&#237;vel Superior (CAPES) - Financial Code 001, Funda&#231;&#227;o de Amparo &#224; Pesquisa do Estado do Rio de Janeiro (FAPERJ), and Instituto Nacional de Ci&#234;ncia e Tecnologia de Fluidos Complexos (INCT-FCx) together with Funda&#231;&#227;o de Amparo &#224; Pesquisa do Estado de S&#227;o Paulo (FAPESP). B.P. was supported by a JCNE grant from FAPERJ.

Human blood samples were provided by adult men and women volunteers according to protocols approved by the Research Ethics Committee of the Federal University of Rio de Janeiro (Protocol 2.889.952) and registered in Brazil Platform under CAAE number 88140418.5.0000.5699. A written form of consent was issued to and collected from all volunteers. Those with any hemoglobinopathy and/or taking controlled medication were excluded. The entire process followed the guidelines approved by the institute&#39;s ethical committee.</p...

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J., Suresh, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Viscoelasticity+of+the+human+red+blood+cell.">Viscoelasticity of the human red blood cell.</a> American Journal of Physiology Cell Physiology. 293 (2), 597-605 (2007).</li><li>Gomez, F., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Effect+of+cell+geometry+in+the+evaluation+of+erythrocyte+viscoelastic+properties.">Effect of cell geometry in the evaluation of erythrocyte viscoelastic properties.</a> Physical Review E. 101 (6-1), 062403 (2020).</li><li>Gomez, F., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Plasmodium+falciparum+maturation+across+the+intra-erythrocytic+cycle+shifts+the+soft+glassy+viscoelastic+properties+of+red+blood+cells+from+a+liquid-like+towards+a+solid-like+behavior.">Plasmodium falciparum maturation across the intra-erythrocytic cycle shifts the soft glassy viscoelastic properties of red blood cells from a liquid-like towards a solid-like behavior.</a> Experimental Cell Research. 397 (2), 112370 (2020).</li><li>Pompeu, P., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Protocol+to+measure+the+membrane+tension+and+bending+modulus+of+cells+using+optical+tweezers+and+scanning+electron+microscopy.">Protocol to measure the membrane tension and bending modulus of cells using optical tweezers and scanning electron microscopy.</a> STAR Protocols. 2 (1), 100283 (2021).</li><li>Agero, U., Mesquita, L. 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The authors have no financial interests in the products described in this manuscript and have nothing else to disclose.

In this protocol, an integrated method based on optical tweezers and defocusing microscopy is presented to quantitatively map the viscoelastic properties of RBCs. Results for the storage and loss shear moduli, together with the scaling exponent that characterizes the soft glassy rheology of RBC are determined. Application of this protocol for different experimental conditions, such as in physiological situation8 or along each stage of P. falciparum intra-erythrocytic cycle<sup class="xref...

Mature red blood cells (RBCs), also known as erythrocytes, are able to extend more than twice their size when passing through the narrowest capillaries of the human body1. Such capacity is attributed to their unique ability to deform when subjected to external loads.
In recent years, different studies have characterized this feature in RBC surfaces2,3. The area of physics that describes the elastic and viscous responses of materials due to external loads is called rheology. In general, when an external force is applied, the resulting deformation depends on the material&#39;s properties and can be divided into elastic deformations, that store energy, or viscous deformations, that dissipate energy4. All cells, including RBCs, exhibit a viscoelastic behavior; in other words, energy is both stored and dissipated. The viscoelastic response of a cell can thus be characterized by its complex shear modulus G*(&#969;) = G&#39;(&#969;) + iG&#34;(&#969;), where G&#39;&#160;(&#969;) is the storage modulus, related to the elastic behavior, and G&#34; (&#969;)&#160;is the loss modulus, related to its viscosity4. Moreover, phenomenological models have been used to describe cell responses, one of the most used is called the soft glassy rheology model5, characterized by a power-law dependence of the complex shear modulus with the load frequency.
Single-cell-based methods have been employed to characterize the viscoelastic properties of RBCs, by applying force and measuring displacement as a function of the imposed load2,3. However, for the complex shear modulus, few results can be found in the literature. Using dynamic light scattering, values for RBC storage and loss moduli were reported varying from 0.01-1 Pa, in the frequency range of 1-100 Hz6. By using optical magnetic twisting cytometry, an apparent complex elastic modulus was obtained7, and for comparison purposes, a multiplicative factor was claimed to possibly clarify the discrepancies.
More recently, a new methodology based on optical tweezers (OT) together with defocusing microscopy (DM), as an integrated tool to quantitatively map the storage and loss of shear moduli of human erythrocytes over time-dependent loads, was established8,9. In addition, a soft glassy rheology model was used to fit the results and obtain a power-law coefficient that characterizes the RBCs8,9.
Overall, the developed methodology8,9, the protocol for which is described in detail below, clarifies previous discrepancies by using the measured values for the form factor, Ff, that relates forces and deformations to stresses and strains in the RBC surface and can be utilized as a novel diagnostic method capable of quantitatively determining the viscoelastic parameters and soft glassy features of RBCs obtained from individuals with different blood pathologies. Such characterization, using the protocol described below, may open up new possibilities to understand the behavior of RBCs from a mechanobiological perspective.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>35mm culture dishes</td>
			<td>Corning</td>
			<td>430165</td>
			<td></td>
		</tr>
		<tr>
			<td>Bovine serum albumin</td>
			<td>Sigma-Aldrich</td>
			<td>A9418</td>
			<td></td>
		</tr>
		<tr>
			<td>Coverslips</td>
			<td>Knittel Glass</td>
			<td>VD12460Y1A.01 and VD12432Y1A.01</td>
			<td></td>
		</tr>
		<tr>
			<td>Glass-bottom dishes</td>
			<td>MatTek Life Sciences</td>
			<td>P35G-0-10-C</td>
			<td></td>
		</tr>
		<tr>
			<td>Glucose</td>
			<td>Sigma-Aldrich</td>
			<td>G7021</td>
			<td></td>
		</tr>
		<tr>
			<td>ImageJ</td>
			<td>NIH</td>
			<td>https://imagej.nih.gov/ij/</td>
			<td></td>
		</tr>
		<tr>
			<td>Immersion oil</td>
			<td>Nikon</td>
			<td>MXA22165</td>
			<td></td>
		</tr>
		<tr>
			<td>Inverted microscope</td>
			<td>Nikon</td>
			<td>Eclipse TE300</td>
			<td></td>
		</tr>
		<tr>
			<td>KaleidaGraph</td>
			<td>Synergy Software</td>
			<td>https://www.synergy.com/</td>
			<td></td>
		</tr>
		<tr>
			<td>KCl</td>
			<td>Sigma-Aldrich</td>
			<td>P5405</td>
			<td></td>
		</tr>
		<tr>
			<td>KH2PO4</td>
			<td>Sigma-Aldrich</td>
			<td>P5655</td>
			<td></td>
		</tr>
		<tr>
			<td>Microscope camera</td>
			<td>Hamamatsu</td>
			<td>C11440-10C</td>
			<td></td>
		</tr>
		<tr>
			<td>Na2HPO4</td>
			<td>Sigma-Aldrich</td>
			<td>S5136</td>
			<td></td>
		</tr>
		<tr>
			<td>NaCl</td>
			<td>Sigma-Aldrich</td>
			<td>S5886</td>
			<td></td>
		</tr>
		<tr>
			<td>Neubauer chamber</td>
			<td>Sigma-Aldrich</td>
			<td>BR717805-1EA</td>
			<td></td>
		</tr>
		<tr>
			<td>Objective lens</td>
			<td>Nikon</td>
			<td>PLAN APO 100X 1.4 NA DIC H; PLAN APO 60x 1.4 NA DIC H and Plan APO 10x XXNA PH2</td>
			<td></td>
		</tr>
		<tr>
			<td>Optical table</td>
			<td>Thorlabs</td>
			<td>T1020CK</td>
			<td></td>
		</tr>
		<tr>
			<td>OT laser</td>
			<td>IPG Photonics</td>
			<td>YLR-5-1064-LP</td>
			<td></td>
		</tr>
		<tr>
			<td>Polystyrene microspheres</td>
			<td>Polysciences</td>
			<td>17134-15</td>
			<td></td>
		</tr>
		<tr>
			<td>rubber ring</td>
			<td>Forever Seals</td>
			<td>NBR O-Ring</td>
			<td></td>
		</tr>
		<tr>
			<td>Silicone grease</td>
			<td>Dow Corning</td>
			<td>Z273554</td>
			<td></td>
		</tr>
		<tr>
			<td>Stage positioning</td>
			<td>PI</td>
			<td>P-545.3R8S</td>
			<td></td>
		</tr>
		<tr>
			<td>Pipette</td>
			<td>Gilson</td>
			<td>P1000</td>
			<td></td>
		</tr>
	</tbody>
</table>

quantitative analysis of viscoelastic properties of red blood cells using optical tweezers and defocusing microscopy

The viscoelastic properties of erythrocytes have been investigated by a range of techniques. However, the reported experimental data vary. This is not only attributed to the normal variability of cells, but also to the differences in methods and models of cell response. Here, an integrated protocol using optical tweezers and defocusing microscopy is employed to obtain the rheological features of red blood cells in the frequency range of 1 Hz to 35 Hz. While optical tweezers are utilized to measure the erythrocyte-complex elastic constant, defocusing microscopy is able to obtain the cell height profile, volume, and its form factor a parameter that allows conversion of complex elastic constant into complex shear modulus. Moreover, applying a soft glassy rheology model, the scaling exponent for both moduli can be obtained. The developed methodology allows to explore the mechanical behavior of red blood cells, characterizing their viscoelastic parameters, obtained under well-defined experimental conditions, for several physiological and pathological conditions.

Figure 1&#160;represents the schematics of the OT system used for the rheology measurements. Figure 2 shows the schematics of the microrheology experiment with both spheres and a representative RBC is also shown. Figure 3 shows a typical curve for the amplitudes of both spheres as a function of time when the sinusoidal movements are produced by the piezoelectric stage. While the reference sphere (Figure 3</stron...

Watch this Scientific Journal Video about Quantitative Analysis of Viscoelastic Properties of Red Blood Cells Using Optical Tweezers and Defocusing Microscopy at JoVE.com

Quantitative Analysis of Viscoelastic Properties of Red Blood Cells Using Optical Tweezers and Defocusing Microscopy

Here, an integrated protocol based on optical tweezers and defocusing microscopy is described to measure the rheological properties of cells. This protocol has wide applicability in studying the viscoelastic properties of erythrocytes under variable physio-pathological conditions.

The viscoelastic properties of erythrocytes have been investigated by a range of techniques. However, the reported experimental data vary. This is not ...

This methodology allows to explore the mechanical behavior of erythrocytes, characterizing their viscoelastic parameters and soft glassy features for several physiological and pathological conditions. Our single-cell based method verifies video references by using the metal values for the form factor that relates forces and displacements, the stresses and scrapes in the erythrocyte surface. Begin by pouring silicone grease over the rubber ring surface in a way that covers the entire perimeter.Next, place the rubber ring on the coverslip with the grease side facing the coverslip. Wait for five minutes for proper attachment, and the sample holders are then ready to receive the cell culture. Next, with the solution of cells previously prepared following the written protocol, seed the cells in the sample holder.Add 0.2 microliters of a 10%volume by volume polystyrene sphere solution to the sample. Place the second coverslip above the rubber ring. Close the setup and finish the sample preparation.Finally, move the entire sample to the microscope. To start with the experimentation, use the OT system, trap the sphere with the OT laser, and then attach it to the coverslip, close to the cell. Then, trap another sphere and repeat the same attachment procedure by pressing the sphere against the cell surface, near the top surface and close to the cell edge.Add a sinusoidal function of amplitude and varying frequencies. Next, press the start"button, using the piezoelectric stage to allow the piezoelectric displacement. Keep the RBC sphere in the trap and submit the sample to a cycle of movements using the previously set sinusoidal function.For analysis, open the ImageJ software and import the entire movie obtained during the sinusoidal movements. Click on adjust, and then select option threshold. Adjust the threshold with both scroll bars, and select the reference sphere by clicking on file, followed by rectangle.Then in the analyze tab, click on set measurements"and select the center of mass"option. Click again on the analyze tab and select analyze particles. A new window containing a table with xy coordinates for the center of the mass will appear.Repeat the procedure for the other sphere attached to the RBC surface. Open the analysis software and import the txt files previously obtained. Generate a plot with the centers of mass on the y-axis and time on the x-axis.Plot the results on a graph using the x-axis for loss constant, denoted by K double prime, and the y-axis for storage constant, denoted by K prime. First, for video acquisition, move the piezoelectric stage in the xy direction, using the software to search for an isolated cell attached to the coverslip. Trap and attach a polystyrene sphere of known diameter to the RBC surface.Next, using the piezoelectric stage, move the trapped bead attached to the RBC surface to deform the cell, and then attach the bead to the coverlip. Now, change the z-axis position to find the focused image. After fixing the position, use the camera software to create a movie of the entire cell.Then, move the z-axis position two micrometers down or up to obtain a defocused image for the chosen cell. Finally, without changing the z-axis position, search for a region without cells to repeat the same procedure, and create a movie of the image background. For contrast image acquisition, first find the value of N zero, click on the polygon selection icon, then click on the analyze tab and select measure.Next, use the contrast equation to determine N image minus N zero, and execute this by selecting math"under process, followed by subtract. Later, divide the result by N zero minus B.Finally, find the contrast for the focused and defocused images. Now, use the Hartley transform to obtain the RBC thickness.In ImageJ, click on process, followed by FFT"and FFT options, and then choose FHT. Then perform the inverse transform FHT by selecting process, followed by FFT"and FFT. Use the resulting image to obtain the height profile.After finding the image that contains the RBC height profile use the two micrometers defocused contrast to create a set of two images in ImageJ. To find the form factor, use an ImageJ customized macro to analyze the stack. The macro will deliver a table with the edge's position, the perimeter, the inverse of the perimeter, and an image of the analyzed cell.Check whether the edges of this image are similar to the edges of the reference figure. Otherwise, repeat the procedure, and use the sum of the inverse of the perimeter to find the form factor. Start by organizing the experimental data in a table.Create a new table in the analysis software by clicking on the file tab. Determine 10 different columns for the parameters. To plot the curve G prime and G double prime in the analysis software, use the data from the previous table and click on the plot"button.To obtain parameters Gamma and GM, click on the curve fit tab and select fit1"to open a new window. Select the square, click on the define button, and type the equation. Click on the okay"button in both the windows, and the fitting will appear.Next, create two other plots, namely G prime and G double prime as a function of omega. Place the error bars only on the y-axis, as previously demonstrated. Repeat the curve fitting procedure, select G"option.Click curve definition"under general fit, and then write the concerned equation. Finally, click on okay, and a curve fitting will appear along with the values for Alpha and G zero. Again, perform another curve fitting procedure.Select G"option, click curve definition"under general fit, and then write the concerned equation. Finally, click on okay, and a curve fitting will appear. The figure shows the storage elastic constant as a function of the loss elastic constant.The linear dependence observed demonstrates that the RBC surface can be considered a soft glassy material. By applying the values for overall cell form factor and RBC surface thickness, the values for the exponent Alpha can be determined. This technique may provide the basis for novel diagnostic methods that correlates changes in erythrocytes'viscoelastic properties with modifications in blood flow of individuals with different pathologies.

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1.2K visualizações.  Universidade Federal do Rio de Janeiro. Esta metodologia permite explorar o comportamento mecânico dos eritrócitos, caracterizando seus parâmetros viscoelásticos e características vítreas moles para diversas condições fisiológicas e patológicas. Nosso método baseado em célula única verifica referências de vídeo usando os valores de metal para o fator de forma que relaciona forças e deslocamentos, as tensões e raspagens na superfície do eritrócito. Comece despejando graxa de silicone sobre a superfície do anel de...