Proc. NatL Acad. Sci. USAVol. 79, pp. 7297-7301, December 1982Biophysics

Transient kinetics of the rapid shape change of unstirred humanblood platelets stimulated with ADP

(stopped-flow laser turbidimetry/rate constants/contraction/Poisson process)

DAVID A. DERANLEAU, DANIEL DUBLER, CHRISTOPH ROTHEN, AND ERNST F. LUSCHERTheodor Kocher Institute, University of Berne, CH-3012 Bern, Switzerland

Communicated by Earl W. Davie, September 15, 1982

ABSTRACT Unstirred (isotropic) suspensions ofhuman bloodplatelets stimulated with ADP in a stopped-flow laser turbidim-eter exhibit a distinct extinction maximum during the course oftheclassical rapid conversion of initially smooth flat discoid cells tosmaller-body spiny spheres. This implies the existence of a tran-sient intermediate having a larger average light scattering crosssection (extinction coefficient) than either the disc or the spinysphere. Monophasic extinction increases reaching the same finalvalue were observed when either discoid or spiny sphere plateletswere converted to smooth spheres by treatment with chlorprom-azine, and sphering of discoid cells was accompanied by a largertotal extinction change than the retraction of pseudopods by al-ready spherical cells. These and other results suggest that theADP-induced transient state represents platelets that are approx-imately as "spherical" as the irregular spiny sphere but lack thecharacteristic long pseudopods and as a consequence are largerbodied. Fitting the ADP progress curves to the series reactionA-- B-+ C by means ofthe light scattering equivalent of the Beer-Lambert law yielded scattering cross sections that are consistentwith this explanation. The rate constants for the two reaction stepswere identical, indicating that ADP activation corresponds to acontinuous random (Poisson) process with successive apparentstates "disc," "sphere," and "spiny sphere," whose individualprobabilities are determined by a single rate-limiting step.

Circulating blood platelets respond to a large number of phys-iological stimuli by forming aggregates, which are essential tothe formation of a hemostatic plug. This normally prevents fur-ther loss of blood at the site of a small vascular injury, but ba-sically the same process can lead to the occlusion of a bloodvessel (thrombosis). Aggregation in vitro is generally precededby rapid changes in cell shape that are accompanied by alter-ations in the apparent light transmission of platelet suspensions(1, 2), and typically flat discoid platelets exposed to ADP orthrombin are converted to smaller, irregularly spherical formshaving a number of prominent long thin pseudopodia (spinyspheres).The present work represents an attempt to examine the shape

changes in real time by using improved turbidimetric methods.Such methods offer distinct advantages over ordinary light mi-croscopy in the determination of overall average size and shapeparameters (3) and avoid often questionable assumptions arisingfrom the use of time-dependent sampling and fixation for sub-sequent analysis. In contrast to microscopy, however, it is dif-ficult to resolve the effects of relatively small scattering centersturbidimetrically because they contribute little to the total scat-tering in comparison to size and shape effects. In this com-munication we infer the existence of a short-lived intermediatein the rapid shape change reaction, and we use the results of

light scattering theory to assign to the intermediate a sphericalshape without long filiform pseudopods. The shape change foreach individual platelet appears to be a continuous (Poisson)process, and the "intermediate" is merely that state of the con-tinuous transformation that has the largest extinction coeffi-cient. Nevertheless, the average dimensions that characterizethe intermediate must differ considerably from either the initialsmooth discoid forms or the smaller and often irregular"spheres" with multiple long projections that are observed asthe result of the completed rapid shape change. It should beclear that the presence of pseudopods in the very early stagesof formation or the presence of surface irregularities that aremuch smaller than the platelet as a whole are not ruled out aspossible features of this intermediate state, nor are changes inthe spatial distribution of small but possibly efficient scattererssuch as dense bodies. The resolution of such details is the prov-ince of microscopy; our interest here concerns the major phys-ical features of the shape change and particularly the dynamicsof the process.

Current methods for following the shape change by turbi-dimetry generally employ relatively high platelet concentra-tions and stirring. Platelets aggregate strongly under these con-ditions, and it is common to prevent this by the addition of 1-4 mM EDTA (4). However, EDTA itself may alter the nativestate of platelets, and rapid development of pseudopods andsurface irregularities as well as changes in internal structure andlight transmission are among the reported effects (5, 6). Stirreddiscoid platelets also exhibit large orientation-dependent trans-mission changes, which virtually disappear upon conversion ofthese cells to spheres or spiny spheres (7, 8). Orientation, ag-gregation, and EDTA-induced effects may all overlap with andmask the small optical signals due to shape change proper,making it a formidable task to analyze the progress curves interms of the fundamental particle extinction coefficients andkinetic rate constants that characterize the reaction. In addition,the apparatus geometry is critical if the last two parameters areto be compared with light scattering and reaction rate theories.In sharp contrast to the case ofabsorbing samples, in which partof the incident light actually disappears during passage throughthe sample, light transmission for the purpose of scattering cal-culations is rigorously defined as the fraction of light transmit-ted along a highly collimated beam in the direction of the beamitself (9-11). Scattering by large particles such as platelets isoverwhelmingly in the forward direction, and unless a beamstop is inserted in the optical train to prevent it, the detectorwill collect an appreciable fraction of the light scattered outsidethe dimensions of the collimated beam and give rise to spurioustransmission values.The present study utilizes stopped-flow mixing of activator

with a diluted suspension of platelets and employs a "zero de-

Abbreviation: CPZ, chlorpromazine.

7297

The publication costs ofthis article were defrayed in part by page chargepayment. This article must therefore be hereby marked "advertise-ment" in accordance with 18 U. S. C. §1734 solely to indicate this fact.

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7298 Biophysics: Deranleau et al.

gree" turbidimeter, which limits the detected light to the di-mensions of the incident (laser) beam. The absence of stirringensures that shape-related orientation effects will be mini-mized, and, in combination with dilution of the platelet sus-pension, it eliminates aggregation and the need to add EDTA.This experimental approach differs significantly from previousattempts to characterize the shape change-by turbidimetry, andit cannot be too strongly emphasized that the progress curvesgiven here are not necessarily comparable with progress curvesobtained by -using other instrumentation.

EXPERIMENTAL PROCEDURESFresh blood from volunteers was collected into citrate, andplatelet-rich plasma was prepared immediately (4). All furtheroperations were done at 370C. After incubating the cell sus-pension with gentle swirling to allow time for any stressed cellsto spontaneously revert to the flat discoid form characteristicofthe resting state [axial ratio 0.26 (12)], it was diluted to 40,000platelets per ul with 26 mM 2-{[tris(hydroxymethyl)methyl]-amino}ethane sulfonate (Tes) buffer containing 128 mM NaCl,3 mM KCI, 0.06 mM CaCl2, 0.02 mM MgCl2, and glucose at1 mg/ml, pH 7.4, and reincubated with gentle swirling.

Shape changes were initiated by rapidly mixing this plateletsuspension 1:1 with the appropriate effector in a stopped-flowlaser turbidimeter (13), which "sees" on the order of 150,000cells. Progress curves were digitized and recorded at 632.8 nmwith an acceptance half-angle of<0. 030 as described (512 pointsper experiment) (13). The suspensions obeyed the Beer-Lam-bert law at up to 5 times the platelet concentration used here,so that secondary scattering is absent or its effects can be ne-glected (10).

Platelet morphology (approximate size, shape) was evaluatedseparately by ordinary light and phase-contrast photomicros-copy for each type ofstopped-flow experiment described, usingboth untreated and glutaraldehyde-fixed samples. Neither ag-gregation nor microaggregation occurred, and because ADPdoes not induce the release of storage granule contents underthe present conditions (14), extinction changes arising fromthese sources can be excluded.

C..0(i.C4..

*C

2C~

Platelet shape was further evaluated by using alternate stir/nonstir cycles in an unsophisticated turbidimeter (noncolli-mated beam, no beam stop): the light transmission of asym-metric cells changes-markedly upon stirring, whereas the lighttransmission of spherically symmetric cells is independent ofstirring (7,;8).

RESULTS AND DISCUSSIONInitially discoid platelets rapidly. mixed with buffer in thestopped-flow apparatus remained discoid on the basis of bothmicroscopic examination and their ability to elicit large changesin apparent light transmission upon stirring. Except for an initialshort. relaxation effect (13),Athe extinction E [= -log(trans-mission)] did not change appreciably during the time rangesconsidered (Fig. la); evidently stopped-flow treatment itselfdoes not lead to any changes in platelet size or shape. The ex-tinction of discoid platelets mixed with chlorpromazine (CPZ)increased monotonically and leveled off after about 3 min (Fig.la). Microscopic examination immediately after stopped-flowmixing showed that the cells had been converted to approxi-mately spherical particles with no projecting blebs or spikes.The apparent light transmission of these cells was insensitiveto stirring, indicating that they are in fact spherical. Such be-havior is just that which is predicted by light scattering theory(7) and previously measured and reported by Latimer et at (8).When discoid platelets were mixed withADP in the stopped-

flow apparatus the extinction also increased at first, but the rateof increase was much faster than with CPZ and the extinctionwent through a well-defined maximum before leveling off(Fig.lb). The progress curve is reminiscent of curves obtained byadding ADP to a stirred suspension of EDTA-treated plateletsin a simple turbidimeter (5) but is independent of the effectsof stirring, EDTA addition, or collection ofunwanted scatteredlight. The final state was characterized in the light microscopeby the appearance of small spiny spheres with numerous longpseudopodia, which are the typical result of the classical rapidshape change. As might be expected from examining scanningelectron photomicrographs of such cells, stirring producedsmall but noticeable alterations in the apparent light transmis-

a

0.101

0.05 1

0

0 100 0 100 0 100

Time, sec

FIG. 1. Typical stopped-flow-progress curves showing the fractional change in extinction (E - EO)/EO, -in which EO is the initial value, observedwhen: (a) fresh discoid platelets are rapidly mixed with buffer or converted to spheroid platelets by mixing with chlorpromazine (CPZ); (b) discoidplatelets are converted to spiny spheres by mixing with ADP; (c) spiny sphere platelets (discoid platelets pretreated with ADP) are converted tospheroid platelets by mixing with CPZ (pseudopod retraction). The broken lines show the approximate behavior of the curves continued along therespective time axes. Final concentrations: platelets, 20,000 per jl; ADP, 5 tuM; CPZ, 100 ,uM.

Proc. Natl. Acad. Sci. USA 79 (1982)

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Proc. Natl Acad. Sci. USA 79 (1982) 7299

sion. Similar results were obtained by using low concentrationsof thrombin (ca. 0.01 unit/ml) that were sufficient to activatethe shape change but not release or aggregation. Platelets pre-viously activated by stopped-flow mixing with ADP largely re-gained their discoid shapes after gentle swirling for an hour ormore and could subsequently be reactivated in the samemanner.The final extinction resulting from ADP action on discoid

platelets was significantly less than that resulting from CPZ ac-tion, presumably because (8) the small body of the spiny spherescatters less light than the larger CPZ sphere and scattering bylong thin pseudopodia is negligible in comparison to scatteringfrom the main platelet mass. To test this proposition, we addedCPZ to platelets that had been previously activated to spinyspheres with ADP. Under the microscope, the pseudopods re-tracted and larger spheroidal platelets were formed whose pho-tomicrographs were indistinguishable from those resulting fromthe treatment of discoid platelets with CPZ. The apparent lighttransmission of these cells was insensitive to stirring, so thatlittle or no essential change in axial ratio is associated with CPZ-induced changes in the shape of spiny spheres. The stopped-flow progress curve showed a monotonic increase roughly halfas large as, but similar to and reaching the same final extinctionas, that produced by the action ofCPZ on discoid platelets (cf.Fig. 1 a and c). Pseudopod formation at the expense of the sizeof the central platelet body with no significant change in axialratio corresponds to the reverse of the reaction just describedand must indeed result in a decrease in extinction.The existence ofa maximum in the ADP progress curve dem-

onstrates the presence of a morphologically distinct interme-diate or set ofintermediates characterized by a larger extinctioncoefficient than either the initial disc or the final spiny sphere(15). Total cell volume appears to be conserved during the re-action, so that the difference between at least the initial and finalextinctions must be mainly due to shape changes (4, 5, 7, 8, 16,17). We assume for the moment that this applies to the inter-mediate as well, and we offer the following tentative interpre-tation of the results in Fig. 1.A true sphere scatters more light (has a higher extinction

coefficient) than any other shape of the same volume, and largespheres scatter more light than small spheres (9, 10). Thereforeit seems likely that the initial extinction increase induced byADP represents sphering of discoid platelets with no effectivechange in body size, and the (smaller) extinction decrease afterthe maximum represents pseudopod formation with a corre-sponding reduction in body size but no change in axial ratio. Forconvenience, we will refer to the intermediate state or statesloosely as a "sphere." The simplest kinetic model consistentwith the above hypothesis is then contained in the idealizedsequence

disc - sphere -2 spiny sphere, [1]

in which k, and k2 are rate constants.The time-dependent extinction due to scattering by such a

system over a unit path is given by the Beer-Lambert law

E(t) = aA(t) + bB(t) + cC(t),

These conditions satisfy the requirements of a unitary (first-or-der) series reaction with concentrations (see, for example, ref.18)

A(t) = AOekit

B(t) = AOk(e-klt -e-k2t)/(k2 - kj)C(t) = AO - A(t)-B(t), [3]

in which AO = A(t = 0) is the initial concentration of discoidplatelets. Combining Eqs. 2 and 3 gives an explicit expressionfor the time dependence of the extinction, which was used tofit the ADP progress curves by standard nonlinear least-squarestechniques (19). A typical fitted curve is shown in Fig. 2 Top.The points are the digitized experimental data, and the solidcurve is calculated from the parameters a, b, c, kj, and k2 thatbest describe these data. The quality of the fit is apparent fromFig. 2 Middle, which shows the same data transformed to zeromean. The absence of significant trends indicates that no arti-facts are present in the fitted portion of the curve. The systemis overdetermined (more than 450 equations in 5 unknowns, seenotes to Table 1), and although the model is preselected, iteither fits (converges to the limit of resolution of a single mea-

0.310 1 1

0.305 [

0.300 k.c4-.

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-0.003 L

1.0 r

4.-

4'

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C

0.5 F

0

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in which a, b, and c are scattering extinction coefficients (crosssections) and A(t), B(t), and C(t) are the concentrations of theindividual states-respectively, the disc, sphere, and spinysphere populations, which are presumed to exist or to be suc-cessively formed according to scheme 1. The reaction rate didnot depend on the ADP concentration at the saturating leveisofADP employed, and the overall reverse rate was much slower(tens of minutes) than the overall forward rate (tens of seconds).

20Time, sec

40

FIG. 2. (Top) Platelet shape change induced by 5 gM ADP. Theobserved (digitized) data are shown as points and the best fit is shownas a solid curve. The first few seconds of the record were not used forcurve fitting because of interference due to the relaxation artifact.(Middle) Same as above but transformed to zero mean. (Bottom) Timedependence of the fractional concentration of discs (A), spheres (B),and spiny spheres (C); A + B + C = 1; 20,000 platelets per pLI. Zerotime is the time at which flow comes to a dead stop in the stopped-flowmixer.

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7300 Biophysics: Deranleau et al.

surement) or does not fit. Fig. 2 Bottom shows the time-de-pendent probabilities (fractional concentrations) of each of thethree states according to Eqs. 3.Mean values for the optical and kinetic parameters that char-

acterize the shape change curves of a single normal donor aregiven in Table 1. The fractional changes in extinction calculatedfrom the fitted extinction coefficient ratios turn out to be vir-tually identical to the corresponding changes predicted by lightscattering theory for idealized shapes. Specifically, our analysisindicates that these are +25% for the disc to sphere and - 10%for the sphere to spiny sphere (pseudopod formation) transfor-mations; scattering theory predicts +24% and -9% for thesesame changes, assuming a platelet volume of 5-10 ,um3 and anaxial ratio of0.26 for the initial disc (7, 8). The assumed volumeand axial ratio are consistent with values estimated for the dis-coid form by direct observation ofresting platelets (12), and theagreement of the predicted and fitted values argues that theintermediate state is indeed roughly spherical and has an ef-fective scattering volume more closely resembling the initialdisc than the final spiny sphere.

It seems highly unlikely that these results can be explainedby a sudden transient change in total cell volume (shrinkage inthis case). One can estimate from ref. 7 and the data in Table1 that more than a third of the cell's total aqueous contentswould have to be pumped out during the first 6 sec of the re-action-and the same amount then pumped back in-to accountfor the time-dependent appearance and the extinction coeffi-cient of the intermediate on the basis of a cellular volumechange. Changes in internal structure involving scattering cen-ters which are small with respect to the platelet as a whole areexpected to have little influence on the transmitted light, al-though they may contribute to the comparatively very weakscattering at large angles (20). Although internal structuralchanges certainly occur (21), there is no adequate means at pres-ent of judging whether these alterations are a feature of theobserved progress curves.

Preliminary microscopic evidence for the existence ofa (moreor less spherical) intermediate in the platelet shape change hasbeen obtained by examination of a series of ADP-treated sam-ples fixed with glutaraldehyde at various times after activation(ref. 22; the data given are for abnormal platelets, but it isclaimed that the same mechanism applies to normal platelets).The intermediate in this case was tentatively described as a"disco-echinocyte" with axial ratio 0.5-0.9, which appears to

Table 1. Optical and kinetic constants of the plateletshape change*

Average values of the fitted decadicextinction coefficients,Pm2/platelet

Average values of the fitted rateconstants,t sec'1

a = 1.4 0.4b = 1.8 0.2c = 1.6 0.2

k, = 0.16 0.01k2 = 0.16 0.01

Ratios of the constants from single fitted a/a = 1curves, averaged over all data setst b/a = 1.25 ± 0.05

c/a = 1.13 ± 0.03k2/k, = 1.0001 ± 0.0007

* Single blood donor (male), eight data sets, not less than 450 individ-ual points per data set. The average residual of the fit, R = X(Ec- E0)/IEo, in which Ec is the calculated and EO the observed ex-tinction, was 0.0020 ± 0.0003 averaged over all data sets. This isequivalent to the fundamental resolution of an individual extinctionmeasurement.

t Average half-life for the speciesA (disc) andB (sphere) 4.5 ± 0.3 sec;average relaxation time 6.2 ± 0.4 sec.

t Averages over internally consistent data sets.

be sufficiently similar to the description arrived at on the basisof the present turbidimetric studies to suppose that both tech-niques are viewing the same basic phenomenon. However,there are significant differences between the two sets of ex-periments. The microscopic study evaluated some 400 plateletsat each of six different reaction times and involves an arbitraryclassification scheme based on specific details, whereas the tur-bidimetric study utilizes a sample size of around 8 x 150,000platelets evaluated at each of 450 or more equally spaced re-action times and involves fitting to a comparatively very simplebut not arbitrary model.

It is highly interesting that the two kinetic constants are thesame, not the least because of the widespread belief that theshape change is a contractile process. The ratio ofthe fitted rateconstants was found to be 1.000 at 31TC and 41TC as well as at370C, so this observation does not appear to be a coincidence.A unitary series reaction involving identical rate constants is ineffect a random process having successive states X0, XI, . . ., XNwith equal transition probabilities, and the integrated rateequations correspond to the Poisson equations

p[X.(t)] = c.(t)/co(O) = (kt)ne-kt/n!, [4]in which p[Xn(t)] is the probability of the state Xn at time t, n= 0, 1, ..., N - 1, and the ci are concentrations. Setting co(t)= A(t), cl(t) = B(t), ..., and using Eqs. 4 in place of Eqs. 3 inthe fitting procedure resulted in a, b, c, and k values that werethe same as those obtained by using Eqs. 3. The Poisson modelis one that is applicable to a wide variety of physical processes,and although in certain biological cases it may break down whenfine details are taken into account (23), it is still a useful ap-proximation. A considerable simplification of the kinetic de-scription is afforded by the use of this model, and it may beparticularly appropriate to the description of a mechanochem-ical process such as the shape change. In the present situationthe stochastic and the classical chemical kinetic models happento be indistinguishable, and it appears that a single rate-limitingstep is responsible for both sphering and pseudopod formation.No information is as yet available concerning the nature of therate-limiting step.

Those attempting to investigate the reaction in more detailmight note that the three states of the simple ABC model arepredicted to have approximately equal probabilities at the pointin time where the probability ofthe intermediate is highest (Fig.2). According to the data in Table 1, this happens at 1/k 6sec, well before the optical response reaches its maximum. Theoptical maximum is displaced toward longer times with respectto the intermediate maximum simply because the final extinc-tion is larger than the initial extinction. In the present case, theoptical maximum occurs at (b - a)/k(b - c) 13 sec (Table 1and ref. 15), at which point the proportion of "discs" to"spheres" to "spiny spheres" is approximately 1:2:4-in otherwords, mainly final product. This raises serious questions aboutthe interpretation (5) of photomicrographs of samples obtainedby fixation at times corresponding to the appearance of the op-tical maximum.

It is instructive to view the shape change kinetics on a log-arithmic time scale, with an eye to eventually sorting out thesequence of biochemical and biomechanical events that takeplace. Stopped-flow mixing of platelets with ADP is completewithin a few milliseconds, and, as shown in Fig. 3, the presentmodel suggests that the disc to sphere transformation first be-comes noticeable after about 50 msec. The interval betweenmixing and the appearance of the first shape change representsthe time required for ADP binding, transmission of the acti-

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Proc. Natl. Acad. Sci. USA 79 (1982) 7301

r-.0tOttto.QzI..OQ.

1.0

.8

.6

.4

di sc

sphere,.2

0

spinysphere

.001 .01 .1 1 10 100 1000Time, sec

FIG. 3. Time dependence of the fraction of discs, spheres, andspiny spheres.

vation signal, and mobilization ofthe components ofthe plateletshape change apparatus. After about a second has elapsed thereaction mixture is expected to contain an increasing proportionof cells with progressively longer pseudopods. A consequence

of our model is that the microtubule ring, which is believed tohelp maintain the shape of the discoid form, must either dis-sociate or be displaced at a rate equal to or greater than the rateof the first shape change.

We thank D. Brugger-Lichtenberg and W. Schnippering for tech-nical assistance, and Drs. H. Patscheke and C. Wuthrich for the mea-

surements on stirred and unstirred platelet suspensions. The work was

supported by the Swiss National Science Foundation, and we are grate-ful to the Emil Barell Foundation of Hoffmann-La Roche for a gift ofsome of the equipment used in the study.

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