Tired and stressed: direct holographic quasi-static stretching of aging echinocytes and discocytes in plasma using optical tweezers [Invited]

Red blood cells (RBCs) undergo a progressive morphological transformation from smooth biconcave discocytes into rounder echinocytes with spicules on their surface during cold storage. The echinocytic morphology impacts RBCs’ ability to flow through narrow sections of the circulation and therefore transfusion of RBC units with a high echinocytic content are thought to have a reduced efficiency. We use an optical tweezers-based technique where we directly trap and measure linear stiffness of RBCs under stress without the use of attached spherical probe particles or microfluidic flow to induce shear. We study RBC deformability with over 50 days of storage performing multiple stretches in blood plasma (serum with cold agglutinins removed to eliminate clotting). In particular, we find that discocytes and echinocytes do not show significant changes in linear stiffness in the small strain limit ( ∼20% change in length) up to day 30 of the storage period, but do find differences between repeated stretches. By day 50 the linear stiffness of discocytes had increased to approximately that measured for echinocytes throughout the entire period of measurements. These changes in stiffness corresponded to recorded morphological changes in the discocytes as they underwent storage lesion. We believe our holographic trapping and direct measurement technique has applications to directly control and quantify forces that stretch other types of cells without the use of attached probes.


Introduction
Blood transfusion is the process of transferring blood products into one's circulation intravenously.Transfusions are used for various medical conditions, to replace lost components of the blood.In many cases this is an emergency procedure and has to be done quickly.The accepted protocol for cold storage of red blood cells (RBCs) in the majority of countries around the world is that they can be stored up to 42 days at 4 • C [1].The "mean 24-hour post-transfusion survival of no less than 75 per cent of transfused red cells" in patients is a major quality consideration in the provision of RBC [2].It has been demonstrated that the safe storage duration depends on the additives and protocols used [3].Some of the protocols that use varying solutions have been shown to influence how RBCs age in vitro.In some of these solutions the storage can be extended to a period longer than 42 days [4,5].The current guidelines in Australia, New Zealand, Canada and most European countries recommend the usage of saline-adenine-glucose-mannitol (SAGM) additive solution which extends the useful shelf-life of the RBCs to be at least 42 days.
Red blood cells are cells responsible for gas transport to/from body tissues [6] using haemoglobin -an iron-containing protein that bonds with oxygen and carbon dioxide.The stability of the shape of RBCs is provided by spectrin and actin protein filaments [7].These proteins form a network that provides mechanical support for the membrane [8].There are many morphological types of RBCs defined by their condition.Discocytes are normal healthy flexible red blood cells named after their biconcave disc-like shape.Other forms of RBCs include echinocytes, stomatocytes, spherocytes, etc. [9].All of these other morphological types are linked to natural aging or various diseases.The flexibility of RBCs is a vital for oxygen circulation in all tissues containing small blood vessels.During their lifetime, RBCs experience repeated deformation when they pass through capillaries in the body.Therefore, measurements of the mechanical properties of RBCs are important for understanding their morphological changes over time.
The RBC membrane and cytoskeleton give the RBC its shape, plasticity and deformability [10].This membrane is composed of a lipid bilayer of phospholipids and cholesterol in which proteins are embedded.The lipids are asymmetrically distributed in each layer and this asymmetry is maintained by adenosine triphosphate (ATP) energized active transport [11].On the intracellular level, interactions between the lipid bilayer and cytoskeleton give the RBCs their useful mechanical properties.On the extracellular level, the receptors and antigenic patterns of the RBC have been observed.RBC membrane structure ensures its cohesiveness during deformation and contributes to the high deformability of RBCs [12].It is important to understand in detail changes in the behaviour of RBCs over time.This knowledge is of great importance for successful RBC transfusions.
Studies have shown that when RBCs lose their capability to deform, it results in shortening of their continued circulation [13].Storage of RBCs results in structural deterioration of membrane components, due to oxidation [14,15], and also ATP depletion [16].It was postulated that extended storage duration following standard blood bank procedures is associated with an overall reduced cell deformability, and impaired cell function after transfusion [17,18].The most visible signs of membrane degradation during aging in storage are shape changes and an increase in the proportion of echinocytes in the unit [19].It is still unclear to what extent membrane components are affected by storage and what contribution storage has on shape changes that could affect RBC function.There is a vast literature that studies the effect of cold storage on the functionality of RBCs [20,21].The validity of established best practices for the storage of the RBCs is debated [22][23][24].
The mechanical properties of RBCs have been investigated using various methods: atomic force microscopy (AFM) [25][26][27], microfluidics [16,28,29], micropipette [30], and optical tweezers [14,[31][32][33][34].The deformability of RBCs has been studied in a number of recent papers, most notably in the paper by McMahon, [35], in which we find a review of existing methods enabling this type of studies.One of the methods monitors the optical (laser) diffraction pattern of RBCs and uses it to determine the change in length and width of a population of RBCs subjected to varying shear stresses.Agraval et al. [36] used dual optical tweezers on single cells to evaluate the degree of elongation.This approach was used to study the deformability of RBCs from type 2 diabetes mellitus (T2DM) patients with or without diabetic retinopathy in comparison to matched healthy controls.A recent review by Zhu et al. (2020) [37] gives a summary of the exploration of single-cell level characteristics and bio-rheological properties of mature red blood cells.In particular, they summarise the study of the efficacy of blood transfusion treatment in sickle cell anemia (SCA).This study was carried out using optical tweezers, where the optically trapped RBCs were dragged in a viscous fluid with varying velocity and RBC elastic response was found by measuring RBC elongation [38].Morphological changes in SCA were clearly observed and compared to healthy blood.Overall Zhu et al. (2020) [37] concluded that OT-based experiments have substantially advanced the understanding of RBC membrane mechanics, intracellular interactions, and cellular constituents.That in turn contributes to building up an understanding of their role in a number of pathological and physiological conditions.
Red blood cells are one of the most studied biological objects using optical tweezers.The aim of most of the optical trapping experiments with RBCs is the investigation of their mechanical properties [1,14,32,39,40].Usually, optical stretching of RBCs is performed by trapping spherical particles and attaching them to the cell.Silva et al. (2012) [14] uses optical tweezers to retain RBCs in a viscous flow, making it a good example of hybrid control of RBC using microfluidics and optical tweezers.Typically, however, there are two scenarios for stretching RBC.In the first scenario, one side of the cell is fixed to the slide and the cell is stretched by moving either the slide or the trapping beam [22,41].Another way of approaching this problem is to attach particles on both sides of the RBC [42] which enables stretching of the cell when the trapping beam is being moved.If the stiffness of the optical trap for a given particle is known, the stretching force can be easily measured by tracking the position of the particle.However, these methods have some disadvantages.Firstly, the point of attachment of the particles to the cell is hard to control.As a result, the stiffness of the cell will depend on the location of the particles and will vary from cell-to-cell.Also, the attachment of the side of the RBC to the slide, as in the first case, complicates the measurements of the length of the cell, as the stretching is performed in a different plane, which distorts the image of the RBC.Secondly, an additional treatment of the sample is required to attach the particles to the RBCs which may change their mechanical properties, create local membrane deformations, and influence the measured stiffness.Alternatively, one can use an optical stretcher [43].The optical stretcher consists of two optical fibres placed opposite to each other creating a counter-propagating trap.By varying the power in each of the fibres, the stretching force can be varied.The calibration of the optical stretcher can be performed by measuring the laser power at which an object escapes the optical trap [44].This can be done only if the drag force acting on the particle is known, as is the case with most microfluidics based experiments.Nevertheless, all these methods require a prior calibration of the detector for each object trapped.
Generally, dual optical tweezers [36,40,45] are an appealing alternative way of investigating RBC elasticity.Their dual beam optical tweezers method was successfully applied to identify differences in deformability in RBC from healthy and diabetic patients [36].Czerwinska et al. (2015) studied RBCs aging in storage using OT and found that deformability decreased during the first three weeks of storage [22].However, the study was not conducted for longer storage duration.It has been shown that the storage lesion occurs in RBCs mostly after the third week of storage [15].Silva et al. (2012) [14] is another important study where RBCs were observed for six weeks.They find evidence that further supports the hypothesis that oxidative damage is one of the mechanisms by which RBCs lose their elastic properties.However, the effect of direct application of optical tweezers onto the RBC structure whilst performing repeated stretching has not been shown.
A direct 3D force measurement method developed by Kashchuk et al. [46] does not require a re-calibration and can be used to measure optical forces on the trapped RBC directly, without attachment of any transducers (such as in the excellent works by [47,48]) or depend on theoretical models of the optical force exerted on trapped cells.Such direct force measurement can be combined with dual optical tweezers to allow transducer-free and model-free measurements of optical forces, and determine mechanical properties of RBCs or other cells.
An extra precaution has to be taken to make sure that the direct trapping of cells does not cause any damage to the cells.Such a study in fact was conducted and showed that the survivability of RBCs was very high [49].Further, the extended confinement of red blood cells by optical tweezers has been shown to be possible without significant thermal damage [14,50,51] and thus the direct force measurement should provide an excellent platform for further in vitro studies involving environmental stressors.
Many mechanical studies on RBCs either measure properties in large blood samples without differentiating between cell morphologies [52] or only consider discocytic cells [53].We study differences in deformability between discocytes and echinocytes using tensile stretching as they age during routine storage using direct force measurement with holographic optical tweezers.Our current study follows RBC mechanical properties of discocytes and echinocytes over the standard 42 days of storage with an additional time point at 50 days to study beyond the regular storage period.This study was undertaken to explain the relationship between deformability, cell morphology and storage duration.Echinocytes undergo changes to their physical properties in storage but much less than discocytes.We show that in the small linear stress limit, discocytes and echinocytes experience little change in compliance over the first 30 days of the observation period.Discocyte stiffness quickly increases to about that of echinocytes by about day 37 whilst echinocytes maintain fairly constant stiffness.This data is comparable to age related increase in Young's modulus found in [18,54,55], where experiments were also conducted in plasma.The optical trapping technique was also able to show that both morphologies stiffen after repeated stretches [56], suggesting an active reaction from the cytoskeleton to prolonged strains.

Red blood cell sample preparation
Leukodepleted packed RBC (pRBC) units and fresh frozen plasma (FFP) units were obtained from the processing department of the Australian Red Cross Lifeblood (ARCL, Kelvin Grove, Brisbane, Australia).
The pRBC units were obtained from whole blood units (450 ± 45 mL) collected into top-andbottom bags containing citrate phosphate dextrose (Macopharma, Mouvaux, Nord, France), and processed within 24 h of collection according to standard ARCL protocols from four donors.After centrifugation (3640 g, 10 min, 22 • C) and leukoreduction, RBC were re-suspended in saline, adenine, glucose and mannitol solution (SAGM, Macopharma, 105 mL).Four pRBC units were obtained on the day after standard processing was completed.
FFP units were obtained from plasmapheresis, using standard ARCL procedures from two donors.Plasma was frozen to −30 • C using a rapid plasma freezer within 24 hours of collection and then stored until required.FFP was depleted of cold agglutinins prior to use, in order to prevent RBC agglutination during storage of RBC suspensions at 4 • C before experiments and to remove floating aggregates that could interfere with the force measurements if trapped with the cells.Both units of A positive FFP were thawed and aseptically pooled.Depletion in cold agglutinins was realised by incubating A positive cells from a single pRBC unit (10 mL) in pooled FFP (35 mL) in 50 mL falcon tubes at 4 • C for 2 hours.The tubes were inverted every 30 min to mix.RBC and agglutinins were removed by centrifuging the suspension (3160 g, 20 min), at 4 • C. The incubation step was completed twice and an extra centrifugation step was added after the second incubation to remove any RBC left in suspension.The clear supernatant was collected and split into 450 mL PVC bags (Macopharma) before being frozen at −30 • C until use.

Holographic optical tweezers
The studies of the optical stretching of unlabelled RBCs are conducted using the dual-beam Optical Tweezers (OT) setup depicted in Figure 1.The force is measured using a position sensitive detector (PSD) by imaging the back focal plane of the condenser onto the PSD.The setup consists of one movable beam and one stationary beam the beams having orthogonal polarisations.In order to move one of the traps, the grating pattern on the Spatial Light Modulator (SLM, P512 Meadowlark Optics) is changed.By applying a pattern to SLM that is similar to a diffraction grating, we can create a movable trap.One trap is movable and the other trap remains stationary (see Figure 2(a)).In order to evaluate the corresponding phase shift ϕ nm for each pixel of the SLM we use the following equation: where ϕ nm is the phase as a function of pixel index on the SLM, x 0 , y 0 is the targeted spot location, and }︂ is the wave-vector of diffracted light.If the light from both trapping beams is reaching the detector, the measured optical force will be zero, as the center of mass of the cell is stationary (on timescales larger than the relaxation time) and the beams exert equal-and-opposite forces.For the measurement of the stretching force it is sufficient and necessary to detect the signal from only one of the beams.The other beam can be filtered out by a polarisation filter just before the detector.The movable beam contains higher order diffraction modes that occur as the result of the construction of the diffraction pattern on the SLM.These higher orders do not apply any force on the cell under study but will contribute to the signal on the detector which will change the results of the measurement.Therefore, we detect the light from the stationary beam.In order to achieve the cleanest signal on the detector we use an iris in the back focal plane of the telescope formed by the condenser and lens L1 (Fig. 1) to filter them out.We use a CMOS camera (MC1362, Mikrotron GmbH) to image and measure the extension of the RBC during stretching.
As is the case for any elongated object in an optical trap once RBC is trapped, it will reorient itself in the trap.This reorientation occurs along the propagation direction of the trapping beams.It is essential to align the two traps horizontally (in the image plane) as only then will the stretching occur in the horizontal plane.The next step is to establish the best starting distance between the two traps to ensure that the orientation of the RBC does not change (which would happen if the two traps are too close to each other) and the RBC experiences no stretching force.After this, the sequence in the measurement is to displace the movable trap further away from the stationary trap.Stretching will occur until the stretching force would become greater than the applied optical force of the movable trap and the cell will escape from the trap instead of being stretched further.We use equal power in the two traps as that gives the best performance.We define the maximum stretching force by the trap with the lowest power.This ensures a uniform stretching of the cell as the same forces are applied to both ends of the RBC.To control the power in each of the two traps, we introduce two half-wave plates (HWP2 and HWP3, Figure 1) and place them before the polarising beamspliter PBS2.The rotation of the waveplate introduces a change in the amount of laser power in each trap individually.The optical force measurements on the RBCs are performed at a 10kHz sampling rate and 10000 points are recorded for each position of the trap.
In order to calibrate the camera we imaged a microscope calibration target that has a welldefined absolute scale.The calibration of the force detector was done by measuring the Brownian motion of a trapped particle and then analysing this motion using the equipartition theorem [57].The pattern on the SLM also needs to be calibrated so that we can determine the step size of the displacement when we move one of the traps.This was done by placing a single spherical particle in each of the two traps (radius, 1.68µm) and subsequently tracking the behaviour with a camera.The distances between several positions of the two particles in the two separate traps were measured corresponding to several series of grating patterns created on the SLM (see Figure 2(b)).This calibration procedure enables us to determine the displacement of the movable trap per integer increase of spatial frequency across the SLM.HWP1, HWP2 and HWP3 are half-waveplates; POL is a polariser.The half-waveplate after the beam splitter PBS1, is required to set the correct polarisation for the SLM pattern.One 1.68µm diameter particle was trapped in each of the dual beams and tracked with a camera.The corresponding distance between the particles was determined for a series of grating patterns (see Figure 2(b)).The measured displacement of the movable trap is measured as 160nm per integer increase of spatial frequency across the SLM.

Determining the extension of stretched red blood cells
The RBCs come in a variety of shapes (discocytes, echinocytes, stomatocytes, etc.) [58].Discocytes are biconcave discs where circumference is larger than height.Optical Tweezers tend to orient these types of objects with the circumference along the direction of the propagation of the trapping beam.During the stretching of the cell in the optical trap, the thickness and the position of the cell will change, leading to a change in the apparent brightness of the cell, confounding tracking algorithms.Another important factor is the stability in the illumination conditions.For example, if there is another cell diffusing into the observation plane or there are some variations in the illumination conditions themselves, the observable signal will change and lead to difficulties in developing a universal algorithm which accurately measures the size of RBCs.
In order to develop a method for consistent measurements of the size of the RBCs, we used the features of our optical system as well as known parameters of the imaging system (see Figure 3).This consists of two steps: The first step is concerned with increasing the contrast of the cell.This is achieved by subtracting the averaged gray-scale value of the background from the image.The absolute value of these values (which can be negative) are taken-resulting in a sharp black border (low gray level) around the RBC.This accounts for the parts of the cell below and above the imaging plane.The second step is to average all of the rows of the image to account for the trapping beams being aligned horizontally (relative to the camera sensor).Figure 3 shows that this gives a noticeable signal (blue curve on Figure 3(c)) which marks the horizontal edges of the cell.In summary, by using interpolation of the object function we can find a region of interest around the cell with sub-pixel resolution.We chose a threshold so that the standard deviation of the pixel data in the image is small enough such that most of each cell type has a region of interest.As we are also trying to measure echinocytes that have irregular shapes we must include as many features as possible in our tracking algorithm.This means finding an outer edge of the RBC.This is not its actual size and thus not usable to determine Young's modulus, but it is sufficient to determine changes in size as the cell is stretched over a chosen range of force-extension to escape from the optical trap, and thus determine the linear stiffness coefficient.For the purposes of this article we call the width of the threshold region the threshold width.

Measurement of the stiffness of RBCs
The main role of the RBCs in the body is transfer of oxygen to the cells and carbon dioxide [59] out of tissues.In the course of this, they experience repeated stretching and bending while travelling through capillaries.Their primary function might be affected if they experience changes in their mechanical properties.Such changes can also lead to a decrease of their lifespan [13,60].When blood products are used for transfusion it is very important to use highly deformable RBCs to reduce adverse transfusion related events in patients.
Sometimes it is of interest to compare the stiffness of the RBCs rather than determining the actual value of the stiffness of each cell in absolute terms.In such a situation we actually do not need the measurement of the length of the cell.In this case, the Direct Force Measurement (DFM) method of the optical force for all the positions of the movable trap can give the change in stiffness.Consider a rigid object which is trapped in a dual-beam optical trap, and has "stretching" forces exerted on it.The object won't stretch (because it is rigid), but will escape from the trap once the movable trap has reached the point of maximum trapping force, which will be located near the edge of the object.If we conduct the same experiment stretching a soft object, the resulting force curve will have a lower slope and the critical distance over which the elastic force will overcome the maximum optical force will be extended.Therefore, we can use the slope of the optical force curve as a measure of the stiffness of the cell over particular intervals of stretching.
Figure 4 shows the extension of the threshold width of the RBC as a function of detected stretching force.A fit of the width of the RBC and measured optical force is overlaid on the data.The linear stiffness coefficient (its structure dependent stiffness, not average material stiffness) of the cell has been found by fitting a linear function into force-length data points for small strains near escape, (k = 9 ± 2 pN µm<sup>-1</sup>).Various assumptions-that are not part of this study-will need to be made to obtain Young's modulus from the linear stiffness [47]; recent developments in understanding the structure of RBCs [61,62] may help with translating our measurements of linear stiffness coefficient to the noted changes in shape.
In order to study the behaviour of the RBCs exposed to prolonged stress and test the damage to the cells (including any effect of heating by the trapping beam and mechanical damage) the cells were repeatedly stretched with dwell times between each extension to allow for cell deformation.Figure 5 shows a result of 20 stretches.Between full cycles in which we restore the cell's shape and align it in the trap, the cell is given 1 s of resting time.Each subsequent position of the movable trap is spaced by a time lag of 200 ms, giving the cell enough time to respond to the changes in mechanical stress [34] and reach equilibrium.The finite bandwidth of the separation of the spots and observation time limits the achievable resolution.We have been able to record three bands of RBC loss corresponding to the three beam separations, 4.16, 4.32, 4.48µm, with frequencies shown in the inset.While there are some deviations in the slope of the force-position curve for repeated stretching, the overall behaviour of the RBC did not change, which implies that the damage to the cell is minimal and is not sufficient to affect measurements of its mechanical properties for smaller numbers of runs.

Mechanical properties of RBCs during storage
The measurements were performed once per week for 50 days (days 2, 9, 16, 23, 30, 37, 42 and 50) using holographic optical tweezers with direct force measurement capability.Five discocytes (includes discocytes and early stage I echinocytes) and five echinocytes (stage II and III echinocytes) were measured for each donor.Each cell was stretched three consecutive times.In order to establish which type of cell was being investigated, the cells were inspected under the high resolution microscope and the decision was made whether it is a discocyte or echinocyte based on their appearance.As outlined in the section on sample treatment and preparation, red blood cells were sampled from units of leukodepleted packed RBCs in saline-adenine-glucose-mannitol solution.Before measurement, the cells were re-suspended in ABO compatible human pooled plasma (i.e., plasma compatible with the ABO blood type of the RBCs).This was carried out in order to reproduce a physiological environment.
We were able to use the gradient of the optical force, linear stiffness-not Young's modulus-as the parameter of between cells.In order to acquire a full force curve enabling the measurement of the stiffness, we stretched each cell until it escaped the trap.Figure 6 shows the average gradient of the measured optical force.
Each time point of our measurements is a mean of stretching five different cells for all four donors (20 cells with three stretches, 60 measurements per cell type per day).Our results in Figure 6 show that the stiffness of discocytes are reasonably stable in human blood serum until Fig. 6.The average gradient of the measured optical force (stiffness) for and discocytes.Stiffness of echinocytes and discocytes are represented by the crosses × and circles •, respectively.Initially, discocytes are more compliant than echinocytes.By day 37 discocyte stiffness is about that of echinocytes.In contrast, echinocyte stiffness is almost unchanged.Modelling the stiffness as constant throughout the time course of experiments works reasonably well for echinocytes with most points within the standard error of the mean.This is not the case for discocytes that show a much larger variation and increasing stiffness.about day 30.After this the stiffness begins to approach that of the echinocytes, about 20% higher than within a few days of collection.Other measurements have shown an increase in the stiffness of discocytes in blood serum [18,54,55].We have noticed that after the third week of storage, echinocytes become the dominant type of the RBCs in the sample.
Figure 7 shows another interesting result: that for each RBC that was studied, the consecutive stretching of it resulted in a larger force for a given separation.If we compare the gradient of the force for each stretch we can see that the slope is increasing for each consecutive stretch-that is, the linear stiffness coefficient or spring constant of the RBCs increases from stretch to stretch.The change in the linear stiffness coefficient is larger for discocytes than for echinocytes.It appeared that discocytes respond to the applied stresses more actively than echinocytes.We repeat stretching one second after the previous one which could indicate that this change could be due to a reduction in the intracellular ATP (adenosine triphosphate) which influences the arrangement of spectrin-a protein that forms a cytoskeleton of the red blood cells.It was previously shown that ATP induces dynamic dissociation of the spectrin filaments and causes rearrangement of the spectrin network [63].This in turn causes softening of the RBC and therefore increases its ability to stretch [64].We see some indication in our data that discocytes become more adversely affected by the slow repeated stretching used in our measurements.The change in stiffness is highly variable and the number of data points is sufficient only to show the stiffness increase between stretches.RBCs were imaged throughout the optical trapping experiments.Using the fitting procedure, we cropped the whole image to center on individual RBCs.We recorded micrographs of the RBCs as they were stretched.Figure 9 shows a sequence of images from one cell of the pRBC units.Throughout our experiments, echinocytes show some change to their shape, but overall maintain their chracteristic 'spiky' appearance.Discocytes, on the other-hand, show significant morphological changes over time.By the second week of experiments, discocytes show recognisable deviations out of their expected biconcave shape.The effect of storage lesion on the morphology is progressive and by the last day of experiments the cells have some protruding features from the surface despite being overall biconcave in shape.Usually, these surface changes occurred in many discocyte cells after the day 30 observation.However, discocytes regain some of their original shape when more significantly stretched.Echinocytes, on the other hand, remain relatively unchanged throughout the time series, occasionally taking on the appearance of stretched discocytes under larger loads.

Discussion and conclusions
We have measured the linear stiffness coefficient (structural stiffness between the trapping points) of aging red blood cells using an optical tweezers direct force measurement technique.The trapping powers used in the experiment were about 40mW, below recognised thermal damage levels [50,65].The ability to directly measure optical forces is powerful.Purely optical deformation of the RBCs avoids the use of attached probe particles/substrates, whilst still allowing repeatable measurements of stretching.Orthogonal polarised laser beams form the optical traps.The trapping signals can thus be effectively filtered to obtain the true force applied to the RBC by using a polariser.Further, when only comparison of the stiffness between the cells is required, the optical forces can be compared directly without measurement of the length of cells that would have been required if we wanted to measure Young's modulus.We had 60 stretches (20 per run) for each cell type on every day the experiment was performed.Cells could be trapped in several trapping positions, and would sometimes fall out of the trap as their shape changed.As a result, some of our measurements were rejected for having too large a sensitivity of the gradient using a p-value statistical rejection (p<0.05 for each fit of a run, plus removal of runs where placement of the bounding box failed) which resulted in about a 15% rejection rate of the 960 runs.The experiment could benefit from increasing the number of stretches per cell or increasing the number of cells studied.There are exciting possibilities for measurements using these techniques to contribute to further understanding and modelling RBC structure [61,62].
We have performed a time series of experiments on RBCs during cold storage carrying measurements up to 50 days past collection.We saw variability between donor samples and compared time series measurements on RBC from all donors.We were able to show that, during the cold storage, the stiffness of the RBCs remains approximately constant until about day 30 for each type.We attribute this to performing the measurements in refined samples (serum) of fresh frozen plasma from donors.After day 30, we noted that local stiffness measurements of discocytes tended toward that of echinocytes.Other measurements have also shown that RBC compliance recovery in artificial serum is only partially successful [16].The response to repeated extended mechanical stress may be an interesting future direction of research using the apparatus we devised for this experiment.
The direct trapping dual beam optical tweezers measurement platform shows excellent prospects for further quantitative experiments of stretching of this and other types of cells.Specifically, when compared to other dual beam optical tweezers methods that use beads and substrate attachment, confounding factors such as contact angle and attachment point variation are avoided.Combined with imaging techniques such as holographic imaging [40] our work lays a foundation for the measurement of multi-point deformation and characterisation of several types of RBCs.

Fig. 1 .
Fig.1.Dual-beam optical trap setup for stretching RBCs.PBS1 and PBS2 are polarising beam splitters used to create two optical traps; SLM is a spatial light modulator; DM1 and DM2 are dichroic mirrors; L1 and L2 are imaging lenses; PSD is a position sensitive detector; HWP1, HWP2 and HWP3 are half-waveplates; POL is a polariser.The half-waveplate after the beam splitter PBS1, is required to set the correct polarisation for the SLM pattern.One 1.68µm diameter particle was trapped in each of the dual beams and tracked with a camera.The corresponding distance between the particles was determined for a series of grating patterns (see Figure2(b)).The measured displacement of the movable trap is measured as 160nm per integer increase of spatial frequency across the SLM.

Fig. 2 .
Fig. 2. (a) The grating pattern on the SLM.The grating gradient controls the position of the trap.(b) Calibration of the displacement of the movable trap by measuring the distance between two trapped particles (silica, d = 1.68µm).

Fig. 3 .
Fig. 3. Steps of the image recognition procedure to measure the length of the RBC.(a) the original image of the RBC.(b) the image with a subtracted background.(c) the bounding box (for determining absolute length change) of the RBC (red lines) is measured by averaging all rows in the image (blue curve) and application of a threshold level so that most cells can be tracked.

Fig. 4 .
Fig. 4. a) Measurements of the stiffness of a particular red blood cell immediately before escape from the optical trap over three runs using the threshold width and optical force detection with fits overlaid.b) Images of the RBC at different displacements from the starting beam position over the three runs.The white scale bar represents 2µm.

Figures 8 (Fig. 7 .
Figures 8(a) and 8(b) present the obtained confocal images from one of the pRBC samples that were used.These images were analysed and measurements extracted using an in-house developed code (Marie-Anne Balanant).Images from a stack were loaded into MATLAB and each image was processed individually.The edges of the cell, corresponding to the RBC membrane, were isolated and smoothed.A number of point coordinates were selected at equally spaced intervals

Fig. 8 .
Fig. 8. Image processing steps from the confocal images to the triangulated mesh of discocytes.Confocal images of a discocyte (a, b), point cloud representing the surface of a discocyte visualised in MATLAB (c, d), Cell surface reconstruction process, from the point cloud to the triangulated mesh (e, f), 3D reconstitution of a discocyte membrane, visualised in MATLAB (g, h).

Fig. 9 .
Fig. 9. False colour images of discocytes and echinocytes with small strains.a) Sequence of discocytes under a small load throughout the time course of experiments in their respective regions of interest.As the storage lesion progresses, the morphology of the discocytes changes away from their expected smooth biconcave shape.b) Sequence of echinocytes at the same points of the experiments.They show less change to their morphology over their storage time.