Determination of cell volume during equilibrium freezing process

REPORTSChinese Science Bulletin 2003 Vol. 48 No.15 1551 554and temperaturel+“，there are no practical experiments toDetermination of cell volumeevaluate the accuracy of those models, especially for thesmall-size cells with irregular/non-spherical shape (suchduring equilibrium freezingas human RBCs and platelets), it is more difficult. Alt-hough water transport during freezing has been exten-processsively studied in single spherical cells together witthe development of cryo-microscopy techniques theseZHAO Gang', HE Liqun', WANG Peitao2,years!7 "10，the central assumption in cryomicroscopyDING Weiping', XIE Xiaojian', LIU Zhong,techniques is that the projected two-dimensional area ofthe cell can be extrapolated to a spherical three-dimen-ZHANG Haifeng , SHU Zhiquan 1,LUO Daweil & GAO Dayong1.4sional volume, while reasonable for spherical cells, thisassumption is inappropriate for obtaining quantitative1. Cryobiomedical Engineering Research Institute, Department of Ther-volumetric information in non-spherical cells.al Science and EnergyEngineering, University of Science andIn this research, a new type electronic particle coun-Technology of China, Hefei 230027, China;. School of Life Sciences, University of Science and Technology ofter was used to determine the volumes of human RBCsChina, Hefei 230027, China;in NaCl solutions of different osmolalities. It was assumed. Red Cross and Blood Center of Hefei, Hefei 230022, China;that the effect of temperature on cell volume can be ne-. Department of Mechanical Engineering， University of Kentucky,glected compared to that of osmolality, the equilibriumLexington, KY 40506-0108, USACorrespondence should be addressed to Zhao Gang (e-mail: cooky@ .freezing point versus osmolality can be obtained accord-mail.ustc.edu.cn)ing to the phase diagram of the binary system sodiumAbstract A new type electronic particle counter EPC,chloride/water, and then the cell volume versus tempera-MultisizerTM 3, Beckman Coulter Inc., USA) was used toture can be gained, thus the above physical model is vali-determine the volumes of human red blood cells (RBCs) indated indirectly, and it suggested that our experimentalNaCl solutions of different osmolalities. The thermodynam-design is practical.ics model describing cell response during freezing process1 Model and numerical simulationwas used to simulate the volume change of RBC in 0.9%NaCl solution during equilibrium freezing process. It wasIn 1963, Mazur developed a mathematical modelassumed that the effect of temperature on cell volume can bebased on thermodynamics principle, which describes cellneglected compared to that of osmolality, then by using thevolume change during freezing processl41. In 1976, it wasphase diagram for the binary system sodium chloride/water,modified by Levin et al. and successfully used in thethe osmolalities of the NaCl solution under different sub-zerostudies of human RBC1. During freezing of cell suspen-temperatures can be obtained (converted from mass concen-sion, ice forms first in the extracellular solution that sus-tration), then the calculated values of RBC volumes can bepended the cells due to the block effect of cell membranevalidated by the experiments.to the growth of ice towards the inside of the ellsl121. TheKeywords: EPC, osmolality, RBC, Van' t Hoff , cell volume.presence of extracellular ice induces a chemical potentialDOI: 10.1360/02ww0315difference across the cell membrane which then causesintracellular water to move towards the extracellular solu-Quantitative determination of the biophysical retion, the consequent reduction in cellular volume wassponse in the target cell is very meaningful during cryo-modelled as fllows11.121.preservation and cryosurgery". It was pointed by Mazur s .dV LpA.RTV-V。AHtwo-factor hypothesis: (1) during slow freezing process,,(1the concentration of extracellular solution increases withBvw" V-Vp +φnVwI mothe growth of extracellular ice, then the cell undergoesEr(1_ 1“solution injury" due to cellular dehydration in higher and4= Lpg expRTTpJhigher concentrated extracellular solution; and (2) duringthe rapid freezing process, it has not enough time for in-where V is the cell volume, T the absolute temperature,tracellular water to outflow through the cell membrane,the permeability of the membrane to water at a referenceintracellular water becomes more and more supercooled,temperature TR，E，the apparent activation energy forthen the cell undergoes“IF injury”(injury caused byintracellular ice formation) due to ice forms inside thehe F中国煤化工as constant, B the coolingcell231. Therefore, an optimal cooling process should berate,CNMH Gvesurface area for waterslow enough to avoid IIF but rapid enough to preventtransMYHGvolume of water, n。thesevere cell shrinkage. Although physical models annumber of moles of solutes in the cell, Vb the osmoticallymathematical equations have been developed and used toinactive cell volume,。(= 2) is the disassociation con-predict cell volume shrinkage as a function of cooling ratestant for salt in water, NH is the heat of fusion of pure iceChinese Sg宇内数剧/letin Vol. 48 No. 15 August 20031551REPORTS(in order to agree with ref. [1], its value is assumed to bewith the deionized water (0 mOsm) and standard NaCl335 m/mg in the temperature range of interest from 0 tosolution (300 mOsm).-20), and Tmo the melting point of pure ice.(.1) The EPC principle.A new type electronicIn order to use the above model, several assumptionsparticle counter was used to measure the mean values ofare necessary as described below": the extracellular solu-human RBCs volumes in NaCl solutions of different os-tion is esentilly infinite compared to the cells, whosemolalities. The EPC principle is an electrical sensing zoneconcentration grads can be neglected; the effective me m-echnique. It is based on measuring changes in electricalbrane surface area available for water transport is constantresistant between two electrodes that are produced whenA. = Ag; the intracellular solution is ideal and dilute; theparticles pass through the sensing zone. The particles passplasma membrane permeability is temperature dependentthrough the zone by being drawn through an apertureand represented by arrhenius relationship (that is eq. (2));under vacuum. Each particle displaces its own volume ofthe heat of fusion of pure ice is constant in the tempera-electrolyte. The volume displaced is measured as a volt-ture of interest; the hydrostatic pressure diference acrossage pulse. The height of each pulse is directly proportion-the cell membrane is zero.al to the volume of the particle, while it has nothing to doIn order to satisfy the condition of equilibriumwith the shape of the particle. The particle concentrationfreezing, the left side of eq. (1) is assumed to be 0, theis controlled and the solution suspending the particlesother parameters are listed in Table 1. Then cell volumesmust be“clean enough" (without or with least noise parti-at different temperatures can be obtained by solving it.cles), which allows the system to count and size particlesfor an exact volume (that is why all the NaCl solutionsTable L Parameter values used in model31used in this research must be filtrated). The software .SymbolValueUnits(Multisizer 3 V3.33) together with EPC can give the per-V74.42μum’centage distribution of the particle amount, volume and40.34*μm3surface area (Multisizer 3 Operator's Manual, PNn1.08x10-14mol .8321681 Rev. A).Lpg17.3x 10-/<1.01325 x 10)m/(9 Pa)(..) Measurement of RBC volumes under dffrentE,16.34 x 10J/molosmolalities. The above prepared RBCs were added into* Data from experiments of this research.different beakers (50 mL) full of NaCl solutions (50 mL)of dfferent osmolalities, numbered 1- 13, equilibratedMaterials and methodsfor 15 min under room temperature. EPC was validated(- ) Human RBC prearation. RBC samples wereusing standard particles (CC Size Standard L10) beforeobtained from a local blood bank (Red Cross and Bloodeach sample was measured. Then the cell suspensionsCenter of Hefei, Anhui Province, China), and used in EPCwere measured one by one using EPC. The software wasexperiments within 24 h. The plasma was removed andset to count 30000 cells each run, every sample wasthe cells were re-suspended in filtrated (PALL- Gelmanmeasured for 5 times (70 um aperture tube was selected inLaboratory, Super- 200, 0.2 μm filtration membrane) 0.9%this measurement). The software then gave the meanNaCl solution. Cell washing processes: RBC suspensionsvolume of the about 30000 RBCs in the sample using itswere centrifuged for 2 min at 2000 g using a centrifugerstatistical module. The mean volumes of 5 runs were av-(Hettich ZENTRIFUGEN, MIKRO2), then the uppereraged to give the last value, which is the equilibratedsolution was removed, and the RBCs were re -suspendedvolume of RBCs under this osmolality.in filtrated 0.9% NaCl solution. This process was repeated3 Result and analysisfor 2 or 3 times (the final cell concentration was about 3i :10/mL).(- ) Freezing point versus osmolality of NaCl solu-.. Preparation of NaCl solutions of different os-tion. NaCl solutions with osmolalities of 118, 185, 260,molalities. NaCl of dfferent mass was dissolved in de-302, 670, 863, 1349, 1583, 1741, 2252, 2682, 2800, 3186ionized water produced by KFLOW-RO50ACB watermOsm have the corresponding mass concentrations ofclean system (KFLOW water system CO., LTD), filtrated0.34%，0.54%， 0.75%，0.88%， 1.92%， 2.46%， 3.80%,using 0.2 μm filtration membrane (PALL Gelman Labo-4.43%，4.85%， 6.18%， 7.27%, 7.57%, 8.52%. Fig. 1ratory, Super-200). Then NaCl solutions of different os-shopoin中国煤化工? between the freezingmolalities 018, 185, 260, 302, 670，863, 1349, 1583,tions of NaCl solutions.1741, 2252, 2682, 2800, 3186 mOsm) were produced, theAcc:TYHc N M H Ghe feeing points of theosmolality values were measured with a freezing pointabove mass concentrations of NaCl solutions can be cal-osmometer Osmomat 030 cryoscopic osmometer, 土5culated, they are -0.26, -0.36, -0.47, -0.54, -1.11,mOsm, German), before the measurement was calibrated-1.42, -2.23, -2.64, -2.92, -3.88, -4.70, - 4.93 and1552Chinese Science Blletin Vol. 48 No. 15 August 2003REPORTS-5.70..1.volume of RBC is about 57% of its isotonic volume,(- i) Obtainment of the osmotic inactive volume V%.which can be compared with our result of DSC methodFig. 2 shows the fine linear relationship between the nor-(about 52%, unpublished). Form the above results, it canmalized RBC volume (relative to isotonic RBC volume)be concluded that the water transport concentrates on theand the reciprocal of normalized osmolality (relative totemperature scale of 0.. 1--4..1. .isotonic osmolality, 302 mOsm in this research). Accord-ing to ref. [3] (P34), Van' t-Haff equation can be written asv1.Vt5.0.60.4 IMass concentration (%)015200.-6--10-12Temperature/ C10525 Lsc2.51.00.5.52.02..0Reciprocal of normalized osmolalityFig. 2. Vari t-Haf plots of human RBC. y = 0.5225x+ 0.5417,R =the cell volume change during freezing process by using0.9713.normal temperature volumes. The advantage of this meth-(.i) RBC volume change during freezing equilibri-od is that it is not restricted by the shape and size of cellsum process. Fig. 3 is the relationship between RBCand that it is simpler and more rapid to be frozen in thevolume and temperature during equilibrium freezing pro-experiment periment. It should be pointed out that thiscess. The real line is the results of the model and the datame中国煤化工1 the L. of the cell is largepoints are the indirect results of EPC method. From Fig. 3,enou二0t too big, for in this case,the EPC method has a good accordance with the forecasttheTHCN M H Gvater flowing out in time.of the model. According to the EPC results, when theIn a word, this method is fully available in the equilibriumosmolality is more than 2500 mOsm, RBC volume has nofreezing process, and it is conditionally available in thefurther shrinkage, which agrees with ref. [15]. The finalquasi-equilibrium freezing process.Chinese Sg宇内数剧/letin Vol. 48 No. 15 August 20031553REPORTS(2) In this research, the applicability of the conven-Chinese Science Bulletin 2003 Vol. 48 No.15 1554.557tional model on iregular/non--spherical cell during equi-librium freezing process is validated by using normalPreparation and characteris-temperature EPC experiments. During cryopreservation oftics of flexible all-organiccells, tissues and organs, non-equilibrium freezing processis widely used except for equilibrium freezing process,thin-film field-effectthis is the direction of further research.Acknowledgements This work was supported by the Chang- JiangtransistorScholar Award, Hundred-Talent Program of the Chinese Academy ofSciences (2000-2003), the National Natural Science Foundation of ChinaQIU Yong, HU Yuanchuan, Dong Guifang,(Grant No.50106016), and the Provincial Natural Science Foundation ofWANG Liduo, Xie Junfeng & MA YaningAnhui Province (Grant Nos. 00047520 and 03043717).ReferencesOrganic Optoelectronic Laboratory . .Department of Chemistry, Tsinghua1. Ramachandra, V. D.,. Debopam, R. Bischof, J. 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