Research Article Oversimplification and ...downloads.hindawi.com/journals/tswj/2014/936202.pdfResearch Article Oversimplification and Overstandardization in Biological Methods: Sperm

Research ArticleOversimplification and Overstandardization in BiologicalMethods Sperm Bioassays in Ecotoxicology as a Case of Studyand a Proposal for Their Reformulation

M A Murado and M A Prieto

Grupo de Reciclado e Valorizacion de Materiais Residuais (REVAL) Instituto de Investigacions Marinas (CSIC)rEduardo Cabello 6 Vigo 36208 Galicia Spain

Correspondence should be addressed to M A Prieto michaelumangelumgmailcom

Received 23 August 2013 Accepted 27 October 2013 Published 6 February 2014

Academic Editors L Bonaccorsi and S Nishizuka

Copyright copy 2014 M A Murado and M A Prieto This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

An interesting toxicological bioassay (fertilization inhibition in sea urchin) uses as assessment criterion a variable (fertilizationratio) whose variation with time creates two types of difficulties First it fails to distinguish between the toxic effect and thespontaneous decline in the sperm activity causing some inconsistencies Second the sensitivity of the fertilization ratio to manyother variables of the system requires a complex standardization constraining the achievement of the method without solving itsmain problemOur proposal consists of using a parameter (spermhalf-life) as the response of the assay and describing explicitly thebehavior of the system as a simultaneous function of dose and timeThis new focus is able to solve the problematic character of theresults based on the fertilization ratio and by using the same data set which is required by the conventional approach it simplifiesthe protocol economizes experimental effort provides unambiguous and robust results and contributes to the detection of anartefactual temperature effect which is not very evident under the usual perspective Potential application of this new approach tothe improvement of other formally similar bioassays is finally suggested

1 Introduction

In the study of biological systems at times a defined gapexists between the recognition of the complexity whichshould be accepted for describing certain phenomena in areasonably realistic way and the oversimplifications oftenapplied to basic problems frequently involving importantpractical consequences Usually such gaps are not justifiedby differences between the levels of study since a simplerapproach from a factual point of view does not involvenecessarily simpler formal tools The more common reasonsargued in this regard are related to the supposed usefulnessof routines which can be solved in practically automaticways to favour their reproducibility However this advantagedisappears whenmdashas it is very usualmdashthe routine leads to the

need of standardizing many variables or whenmdashas it occursoccasionally as wellmdashits original purpose is distorted

Under this perspective we will discuss and propose newfocus for a useful bioassay which is based on the drop of thefertilizing success of free spawners in the presence of a toxicagent and is applied since years ago in the ecotoxicologicalfield This method with interesting capabilities was initiallydesigned for sea urchin in which the immediate formation ofthe fertilizing membrane around the egg makes the detectionof the products of the process easy Afterwards the procedurehas been applied to other organisms such as the coralAcropora millepora [1] or the polychaete Hydroides elegans[2] and it is quite clear that the essence of the bioassaymdashand its problems as wellmdashcan be generalized to very differentsituations from the original one

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 936202 13 pageshttpdxdoiorg1011552014936202

2 The Scientific World Journal

2 Theoretical Background and Methods

21The Conventional Approach The current procedure withprecedents since almost one century ago [3] is a synthesisof those that were developed by Dinnel et al [4ndash6] andPagano et al [7ndash9] and it is recommended at presentby environmental agencies [10] The bioassay involves theexposure of a sperm suspension to increasing levels of atoxic agent during increasing times followed by the additionof an egg suspension to the treated sperm [11 12] Afterthe time required to reach the asymptotic maximum of thefertilization ratio in the absence of the agent (control) theproducts of the process are fixed with formalin and countedSubsequently the toxic effect of the increasing doses of theagent over the fertilization ratio is assessed through any dose-response (DR) model

Thus if1198650and119865119888are the fertilization ratios in the absence

of toxic (control) and at the toxic concentration (dose) 119888respectively the response quantified as 119877 = 1 minus (119865

1198881198650) can

be described with the Weibull dose-response model as anexample which is an especially versatile DR model [13ndash16]Using this equation in a reparametrized form [17ndash19] whichmakes it appropriate in this context we can write

119877 = 119870[1 minus exp(ln 05(119863119898)

119886

)] (1)

where119870 is the asymptotic maximum of 119877119863 the dose119898 thedose corresponding to half-maximum response (119898 = ED

50if

119870 = 1) and 119886 a shape parameter that defines (together with119870 and119898) the maximum slope of the function

It should be underlined that this assay solves elegantlyseveral key issues of the DR analysis (a) it works with alarge population a condition that is difficult to satisfy if thetarget species is not a microorganism (b) it deals with anontogenically essential and physiologically sensitive process(c) it is a fast test avoiding the changes in the physical-chemical system [5] or in the biotic sensitivity [20] which arepossible in longer assays such as those that are focused onlarval growth inhibitions Short times are specially interestingin the assessment of lipophilic toxics whose micelles cancoalesce during the course of static assays lasting a numberof hours causing uncertainty regarding the real dose in theimmediate environment of the organism

However the direct use of the drop in the fertilizationratio as response pays a steep price in practical complicationsand ambiguity of the results both because of the characteris-tics of the system and the structure of its formal treatment

211 Exigencies of the Biologic System Some necessary cau-tions in this regard are of a common kind in many analyticalmethods This is the case for example of the effects of statevariables as temperature and composition (essentially pHand salinity) or the need to use glass material [5] A factthat has also correlates in other methods is the requirementfor maximizing the sensitivity of a fertilization ratio forthe control close to 1 but less than 1 to avoid as much aspossible hiding the toxic effect by a possible excess of spermHowever in a more specific and obstructive way the assay

is affected by particular variables such as (1) the absoluteand relative gamete concentrations (2) the contact time (3)the sperm age (4) the dilution of the system accelerates theconsumption of its limited energy reserve probably due toan increase of respiration and therefore shorts out its lifespan The control of these last factors is difficult becausethe existence of interactions among them [21] preventsthe individualized selection of appropriate values In factstandardization is a customary claim in the bibliographyregarding this method [22ndash24] and other authors [25] evenhave argued the need to use more than one gamete ratio totake into account the reproductive failure due to polyspermy

212 Implications of the Descriptive Approach Under thispoint of view the method shows the following problematicaspects

(1) Although it is recognized that the exposure timeto toxic agent affects the fertilization ratio [5] thisvariable is not formally included into univariate DRmodels as (1) Therefore since each time leads toa different assessment the decision about which ismore representative is arbitrary

(2) The short life span of the gametes makes feasiblea more realistic assay in which the exposure timecover as their entire life period as it occurs in naturalconditionsThe use of briefer exposure times can onlycontribute to increase the error and underestimate thetoxic effect

(3) If the sum of the exposure and contact times does notexceed the sperm life span it could happen (assumingthat the toxic action reduces the sperm activity)that at the end point the fertilization processes areunder different doses at different distances fromtheir respective maxima making any comparisonquestionable

(4) The values of the fertilization ratio 119865 contain infor-mation regarding the effects of the toxic action andthe sperm age but the formal treatment ignores thesecond oneThus the variability linked to both effectsis accumulated only over the toxic action causingtwo undesirable consequences the inaccuracy of theresult and the bias of the parametric estimates

(5) Finally as we will see in the results section tem-perature exerts an inevitable and purely artefactualeffectmdashthat is apart from the one ruled by theArrhenius equationmdashin any assessment through theconventional method

22 Factual Frame of the Assay Fertilization Kinetics Inthe reproductive phenomenology of the sea urchin rich instudies the most of its quantitative behavior both in exper-imental [21] and observational [26] contexts is explained bya fertilization kinetic model which Vogel et al [27] calledmdashacurious tribute toMozartmdashDonOttavioThis model assumesthat the random encounter between gametes follows a secondorder kinetics in which the egg retains a certain number of

The Scientific World Journal 3

0

02

04

06

08

1

0 5 10 15 20

F

Time (min)

(a)

0 5 10 15 20Time (min)

0

02

04

06

08

1

F

(b)

0 5 10 15 200

02

04

06

08

1

F

Time (min)

(c)

Figure 1 Effect of the parameters 120573 and 1205730from (2) on the fertilization kinetics for a constant value of 119878

0(1000120583L) and increasing values

of1198740(1 2 6120583L) (b) Parametric values (120573 = 38 times 10

minus6 1205730= 33 times 10

minus4mm3sdotsminus1) from Vogel et al [27] at left and right results of dividingby 4 the value of 120573 and multiplying by 4 the value of 120573

0 respectively

spermatozoa irrespective of the fertilizing character of theevent Thus the fertilization ratio (119865) 119878

0and 119874

0being the

initial concentrations of gametes can be described as

119865 (119905) = 1 minus expminus120573

1205730

1198780

1198740

[1 minus exp (minus12057301198740119905)] (2)

where the kinetic constants 120573 and 1205730(mm3sdotsminus1 required

volume for a fertilizing rate of one egg per second) are theproduct of the sperm speed by the total (in 120573

0) or effective (in

120573) egg sectionSeveral authors [25 26 28] have pointed out that this

model does not take into account the fertility failures dueto polyspermy induced by high 119866

0= 11987801198740ratios which

produce no asymptotic curves but with a drop after amaximum However this problem is outside the strict kineticprocess and therefore (2) can provide a useful perspective forguiding the assay considered here

If the idea is to base the evaluation on parametricvariations a first option (not very feasible but that needsto be discussed) would be to use the parameters 120573 and 120573

0

of (2) both dependent on the sperm activity which is thesensitive variable of the system As illustrated in Figure 1 thefertilization rate and the asymptotic value of 119865 decrease if 120573does it and the asymptotic value decreases if 120573

0increases

Thus at a given 1198660ratio the kinetic data at different doses

of a toxic agent would able to assess the toxic effect on bothparameters

This approach could be simplified by taking into accountthat at the high 119866

0ratios which are used in practice the

process can be considered as following a pseudo-first orderkinetics In fact all profiles of Figure 1 could be adjusted witha high accuracy (1199032 gt 0999) to the model

119865 = 119865infin[1 minus exp (minus120583 sdot 119905)] (3)

where the parameters 119865infin

and 120583 both potentially sensitive tothe toxic effect are the asymptotic maximum of 119865 and themaximum specific rate of fertilization respectively

However the use of either of these parametric pairs(both 120573 120573

0and 119865

infin 120583) has several disadvantages One is the

sensitivity of the required data measured in a relatively shorttime interval to the experimental error Another one is thedependence of the parametric values on the119866

0ratio (Figure 2

which also shows that the effect of the overall gamete popu-lation becomes less relevant as the contact time increases)Finally the variations of each parametric pair are in generalstrongly correlated Therefore solving separately the kineticand DR models would be a requirement which would resultin losing the advantages of a simultaneous solution as it willbe proposed nextmaking use of another aspect of thework ofVogel et al [27]

23 An Alternative Proposal The main issue of the bioassayhere studied is the fact that the sperm activity declinessimultaneously with age and the toxic action within thesame timeframe and following in both cases a sigmoidalprofile Our proposal consists of accepting this dualism andsubmitting it to a model able to describe simultaneously butin a distinctive way both phenomena It requires defining theresponse not as a function of the fertilization ratio (119865) whichvaries with time but as a function of a time parameter suchas the sperm half-life (120591)

The sperm life spanmdashand therefore its half-lifemdashis deter-mined through the drop of the fertilization ratio with timewhich Vogel et al [27] described with the normal massfunction As this function lacks in the explicit algebraic formthat is required for our purpose we will use theWeibull massfunction that is (1) now in its decreasing form

119865 = 119865119898exp(ln 05( 119905

120591)

V) (4)

where 119865119898is the initial maximum of 119865 119905 is time 120591 is the half-

life and V is the shape parameter It should be noted that 119865varies between amaximumvalue119865

119898at age zero (independent

of the toxic agent because it implies a null exposure time) and


1438

62

14003800

6200

1

08

06

04

02

0

F

S0O0

(a)

1

08

06

04

02

0

1438

62

14003800

6200

F

S0O0

(b)

1

08

06

04

02

00 4000 8000

Total gametes120583L

F

at S0O0 = 100

(c)

Figure 2 Fertilization ratio as a function of gamete concentrations in Paracentrotus lividus ((2) with the central parametric values fromFigure 1) at 2 (a) and 10 minutes (b) (c) Values along the diagonal of the 119878

01198740plane in (a) (∙) and (b) (∘) illustrating the effect of the absolute

gamete population for a single 11987801198740ratio

Time (min)0

1

0

08

06

04

02

20 40 60

F (u

nits)

(a) Data from Vogel et al [27]

Time (units)

F (u

nits)

Time (units)

F (u

nits)

Finfin at age = 0

Finfin at age = t

(b) Relationships between the maxima of 119865 and the spermatic lifespan

Figure 3 (a) Spermatic lifespan (Paracentrotus lividus) in sea water at 18ndash20∘C pH = 82-83 diluted ldquodryrdquo sperm (13000) Data fromVogel et al [27] (points) adjusted to (5) (line) (b) Relationships between the maxima corresponding to the fertilization kinetics (left) andthe spermatic lifespan (right)

a null value when the sperm exhausts its life span (at a dose-dependent time) Thus it can be considered that 119865

119898= 1 and

then expression (4) is reduced to

119865 = exp [ln 05( 119905

120591)

V] (5)

When this equation was applied to the data from [27]the resulting 120591 value of 2509 plusmn 145 minutes was in goodagreement (Figure 3(a)) with the result obtained by theseauthors using the normal distribution (120591 = 250 plusmn 82

minutes)Now if 120591 decreases from a 120591

0value in the absence of toxic

to a 120591 value in the presence of a given dose of the studied toxicthe response 119877

120591can be formulated as

119877120591= 1 minus

120591

1205910

therefore 120591 = 1205910(1 minus 119877

120591) (6)

where 119877120591is (1) Thus the bivariate model

119865 = exp [ln 05( 119905

120591)

V]

120591 = 12059101 minus 119870[1 minus exp(ln 05(119863

119898)

119886

)]

(7)

should provide an unambiguous evaluation of the toxic effecton the sperm half-life

Since 120591 is determined from the maximum value of 119865at different sperm ages from now on a distinction shouldbe made between two maxima of 119865 with different meaning(Figure 3(b)) 119865

infinis the asymptotic maximum of 119865 obtained

after enough contact time (119905infin) at any working conditions for

example at different sperm ages 119865119898is the initial maximum

value corresponding to 119865infin

at the age which is considered aszero

24 Experimental Procedure and Standardization Needs Theexperimental protocol should observe the same cautionsas the conventional one regarding the manipulation of the


gamete suspensions and it differs very little from this lastone regarding its execution In the beginning of the test thefollowingmaterialsmdashvolumes are only indicativemdashshould beprepared (i) a suspension of sperm and another one of eggsat the appropriate concentrations (see below) for the assay(ii) 119899 series of 119896 tubes each 119896 minus 1 doses of the toxic agent in95mL of seawater and one control Under these conditionsthe bioassay involves the following

(1) at time zero to add 100 120583L of the sperm suspension toall tubes

(2) at increasing times (including zero) covering theentire sperm life span estimated for control to initiatefertilization in the corresponding 119899

119894series by adding

400 120583L of the egg suspension(3) after a sufficient contact time to reach in each 119899

119894

series the asymptotic value 119865infin

in control to fix theproducts of the process by adding 100 120583L of formalinsolution

The use of the parameter 120591 instead of the variable 119865as the basis of the assessment offers here another importantadvantage Indeed 119865 is a sensitive value to the initial gameteratio (119866

0= 11987801198740) and in fact in assays based on the

variation of 119865 Dinnel et al [5] stated that the sensitivity tothe toxic agent is inversely correlated with119866

0ratio However

if within a wide range of 1198660values (with constant 119878

0) 119865infin

atage zero (ie 119865

119898) is coded as 1 in all cases the same value of

120591 is obtained which makes this criterion very robust againstvariations of 119866

0ratio

In fact the only particular variable of the system thataffects the sperm half-life is the sperm dilution due to itsrole in the oxygen availability as described by Levitan et al[21]Thus the only condition that determines the appropriate1198660ratio is the need to avoid a sperm excess that could hide

the toxic effect This is achieved if 119865119898

lt 1 what does notprevent to code this value as 1 Dinnel et al [5] used valuesin the reasonable range [06 09] but it should be noted thatthe closer 119865

119898is to 1 the clearer results are obtained

Clarity makes equally advisable low working tempera-tures which extend the sperm half-life and provide a ldquospacerdquo(see Figure 4(B2)) for life spans that are shortened by thetoxic action Later on another important implication of thetemperature will be discussed

The test is also consistent against objections about thepossible effects of polyspermy [25 26 28] because the spermhalf-life is not related to subsequent fertilization failures orlarval malformations (relevant in larval assays) which canderive from a multifertilized egg

25 Numerical Methods for Comparing the Two ApproachesA comparison between the described alternatives through areasonable experimental effort would lack statistical reliabil-ity Another solution is to use simulation experiments withrealistic values including error As we shall see later such asolution is especially appropriate in the present case

Simulations were carried out by assigning concrete para-metric values to model (7) to generate in a Microsoft Excelspreadsheet virtual assays with 8 doses at 7 times including

zero in both cases An ad hoc macro was written to executeseries of 2000 virtual assays each of them involving thefollowing operations (1) addition of a normal homoscedasticerror to the model-generated values of 119865 (2) fitting of theresult to models (1) and (7) to estimate their parameters bynonlinear least squares (quasi-Newton) through the Solvercomplement included into Microsoft Excel (3) calculationof the parametric confidence intervals (Studentrsquos 119905-test with120572 = 05) by applying Solver Aidmacro [29]

To facilitate comparisons doses times and fertilizationratios were coded into the interval [0 1] Since the responseis sigmoidal both as a function of dose and time the valuesof both variables were established according to a geometricprogression with a ratio 119892 = (1119909

1)1(119899minus2) where 119909

1is the

first non-null term of the series and 119899 the number of termsincluding zero The experimental error was simulated withrandom normal numbers 119873 (0 120590) as described previously[30] by using the following expression

119873 (0 120590) = 120590 [(minus2 ln 1199061)12

] sin (21205871199062) (8)

where 1199061and 119906

2are two random uniform numbers as

provided by the spreadsheet The values routinely assignedto 120590 were 005-(0025)-015 and for some cases 120590 = 025

was reached (ie from 5 to 25 of the maximum value ofthe dependent variable 119865) Also for clarity we have usedthe notation CI for the confidence semi-interval as of theparametric value Thus in the usual expression 120579 plusmn CI 120579estimate is statistically significant only when CI lt 100

Since fittings were carried out with 120572 = 005 in theStudentrsquos 119905-test a virtual series is considered statisticallysignificant (95) when 100 of the 2000 repetitions are sig-nificant Now the parametric CI can be calculated accordingto two criteria (1) averaging the CI resulting from the 2000repetitions (2) calculating them (120572 = 005) on the basis ofthe 2000 parametric estimates Although both criteria differvery little the second one is slightly more concessive andit was not applied Skewness and kurtosis coefficients of theparametric distributions were calculated using all estimatessignificant or not Although they are informative values itshould be kept in mind that their basis on the moments ofthird and fourth order tends to exaggerate the effect of themore deviant estimates from mean

3 Results and Discussion

Conventional (M0) and alternative (M1) methods use thesame data sets fertilization ratios (119865

119888119905) at a toxic concentra-

tion 119888 and a time 119905 However the different formal frames inwhich they are processed make the nature of the respectiveresults different

In M0 DRmodel (1) is individually applied at each timeto a response defined as 119877

119865= 1 minus (119865

1198881199051198650119905) that is as the

decreasemdashincreasing with the dosemdashof the fertilization ratioat a given time In M1 model (7) is directly applied to thewhole of the 119865

119888119905values and the response increasing with the

dose as well is the decrease of the sperm half-life As far ashere we have used the same parametric notation (119870119898 119886) inDRmodel (1) and in the DR part (second equation) of model


Table 1 Properties of the parametric estimates obtained by fitting a virtual assay (2000 repetitions) tomodels (1) and (7) the first individuallyapplied at 6 increasing times Negligible experimental error (homoscedastic 120590 = 5 times 10

minus4) and no replicates were supposed CI () averageconfidence interval (120572 = 005) as percentage of the estimate value STS () percentage of statistically significant estimates SK and KTskewness and kurtosis coefficients ALL STS () percentage of fittings in which all the estimates were statistically significant 1199032 correlationcoefficient between simulated and predicted values See also Figure 4

True parametric values [4] Overall fitting to the model [4] Individual fittings to the model [1]1199051

1199052

1199053

1199054

1199055

1199056

120591 0600 0600 mdash mdash mdash mdash mdash mdashCI () 0081 mdash mdash mdash mdash mdash mdashSTS () 1000 mdash mdash mdash mdash mdash mdashSK minus002 mdash mdash mdash mdash mdash mdashKT 007 mdash mdash mdash mdash mdash mdashV 2500 2500 mdash mdash mdash mdash mdash mdashCI () 0105 mdash mdash mdash mdash mdash mdashSTS () 1000 mdash mdash mdash mdash mdash mdashSK 001 mdash mdash mdash mdash mdash mdashKT minus004 mdash mdash mdash mdash mdash mdash119870 0800 0800 0348 0742 0986 1004 1002 1000CI () 0027 160 144 163 205 100 058STS () 1000 1000 1000 1000 1000 1000 1000SK minus006 007 013 minus007 000 minus005 015KT 001 016 minus014 005 016 007 minus011119898 0250 0250 0463 0430 0349 0252 0171 0110CI () 0100 133 130 171 261 172 580STS () 1000 1000 1000 1000 1000 1000 1000SK 006 003 minus020 008 minus003 minus006 minus002KT 007 006 004 011 003 minus005 036119886 2000 2000 4209 3942 3559 3186 2790 2641CI () 0179 648 550 702 1012 738 1740STS () 1000 1000 1000 1000 1000 1000 1000SK 013 000 minus014 009 minus003 minus019 073KT 017 007 minus018 minus002 009 012 198All STS () 1000 1000 1000 1000 1000 1000 10001199032 1000 1000 1000 1000 0999 1000 1000

(7) From now on if necessary we will distinguish betweenboth meanings by using the subscripts 119865 and 120591

The fact that M0 and M1 use the same observationalvalues within different conceptual frames has an importantconsequence for the validation (or refutation) of M1 sincethis approach is under the obligation to explain the resultsfrom M0 as well If it is so the abundant experimentalresults which have led to accept M0 become an experimentalvalidation of M1 And in such a case the selection of oneor another approach is reduced to compare the logicalconsistence of their conclusions as well as the statisticalreliability of results that are affected by the same error in thedependent variable (119865

119888119905)

31 Relationships between the Conventional and AlternativeAssays Firstly to clarify the ideal relationships between thetwo descriptions both were applied to a set of simulationscarried out by assigning the parametric values specified inTable 1 to model (7) supposing an assay without replicates

with a negligible but nonnull error (120590 = 5 times 10minus4) to allow

the running of the statistical testsResults (Table 1 and Figure 4) showed that the assess-

ments derived from the M0 approach are exactly as thosedescribed in bibliography Dinnel et al [5] for exampleworking with silver nitrate as a toxic agent specified that theldquofertilization success was inversely related to sperm exposuretimerdquo and indeed the decrease with time of the values of119898119865(ED50119865

) could be described with a hyperbolic equation(Figure 4(U2)) Such a description however is not veryinteresting since the notion of119898

119865is meaningless both at zero

time and at times beyond the sperm life span preventing theexistence of useful reference points

Since a simulation with model (7) produces throughmodel (1) the typical results of the M0 approach thedescriptive capability above required for accepting M1 isprovenThus it can be stated that a response which increaseswith time in terms of the drop in 119865 arises as a consequence ofa toxic action which reduces the sperm half-life But in such


0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

108

0604020

108

0604

020

1

08

06

04

02

0

F

Dt

0

02

04

06

08

1

0 05 1

F

t

0

02

04

06

08

1

0 05 1

R as

F d

ecre

ase

D

0

02

04

06

08

0 05 1t

Bivariate approach

0

02

04

06

08

1

0 02 04 06 08 1

R as

F d

ecre

ase

D

Conventional univariate approach

U1

U2

B1

B2

B3

B4

t1

t2

t3

t4t5

t6

t1

t2

t3t4

t5

t6

m (E

D50)

Figure 4 Different perspectives of the relationships among dose (119863) exposure time (119905) fertilization ratio (119865) and response (119877) this last onedefined as (increasing) decrease of 120591 or119865 as a function of the dose with respect to the control Simulations frommodel (7) with the parametricvalues are specified in Table 1 supposing a negligible error (120590 = 5 times 10

minus4) The closed symbols in subfigures (B2) and (B3) correspond to thecontrol time course and the complete dose series at time zero respectively The open symbols in subfigures (B2) and (B3) correspond to thedifferent response at different doses of toxic and the different exposure times respectively See text and Table 1 for details

a case the assessment should be based on the variation of thehalf-life parameter because the use as response to the 119865 dropat a given time necessarily leads to a result in which the effectsof the toxic action and the sperm age are confused

This fact is illustrated in Figure 4(B3) which representsthe response to the toxic agent defined as 119877

119865mdashthat is in the

appropriate form for model (1)mdashin the bivariate frame ofmodel (7) In these conditions if intercept is subtracted toeach curve the fittings to model (1) produce the same 119898

119865

values as those obtained using the responses defined withrespect to the control at each time according to the M0

approach But this perspective makes evident that the fallof the fertilizing capability due to the toxic action begins ateach time at a different level determined by the remainingcapability of the sperm at this age Despite the low value of120590 used the CI of the parametric estimates obtained with (1)were 10ndash100 times higher than those produced by (7) Thedegrees of freedom involved in one and anothermodel justifyto a large extent this difference which to a minor extent isdue to the fact that none DR model by itself can explainsatisfactorily the behavior of this system Later we will seeother consequences of the M0 approach


004 008 012 0160

1

2

3

4

004 008 012 016

K m

and

a es

timat

es

K m

and

a es

timat

es

0

1

2

3

4

004 008 012 016 004 008 012 016

No replicatesno smoothing

2 replicatesno smoothing

No replicatessmoothing

2 replicatessmoothing

0

1

2

3

4

004 008 012 016 020 0240

1

2

3

4

004 008 012 016 020 024

2 replicates double smoothing (along D and t variables)2 replicates double smoothing (along D and t variables)

120590 of the observations 120590 of the observations 120590 of the observations 120590 of the observations

120590 of the observations 120590 of the observations

120591an

d

estim

ates

120591an

d

estim

ates

Figure 5 Effect of the observational error on the parametric estimates of model (7) (120591998779 V998795119870119898 ∘ 119886 ◻) and their confidence intervalsunder the specified conditions Dotted lines indicate parametric true values

32 Effects of the Experimental Error The same simulationswere now performed using five different levels of experimen-tal error [120590 = 0050-(0025)-0150] under the four conditionsresulting from combining single or duplicate observationswith raw or smoothed (moving average window = 3) data

As expected in the light of the preceding results model(1) was appreciably more error sensitive In assays withoutreplicates the proportion of repetitions with all significantestimates did not reach 100 at any of the times consideredeven with the lowest error (120590 = 0050) With two replicatesor smoothingwithout replicates 100of significant estimateswere reached at the times 119905

3and 119905

4 By combining two

replicates with smoothing also 100 was found at 1199052 With

120590 = 0100 the model was only significant at 1199052 1199053 andmdashwith

pronounced skewness and kurtosismdash1199054 when besides two

replicates and smoothing the concessive criterion describedin the numerical methods section was applied to the CIcalculation

Model (7) produced instead satisfactory fittings in thetwenty cases (Figure 5 top)The most error-sensitive param-eters were those linked to slopes (V and 119886) 120591119870 and119898 beingremarkably robust In the studied range of 120590 the CI increaseof the parametric estimates was only slightly deviated fromlinearity at the two higher errors in assays without replicateswhere the frequency of statistically significant 119886 estimatesdecreased to 998 and 993Otherwise all the estimatesweresignificant at 100 of the 2000 repetitions The use of tworeplicates reduced markedly the CI (minimal reduction was27 in 119898 and maximal 52 in 119886) increasing at 100 thefrequency of the significant estimates of 119886 with the highesterror Smoothing along the 119863 variable produced equivalentresults and when it was applied with two replicates theCI reductions varied between 31 (120591) and 66 (119886) all theestimates being significant in 100 of repetitions even if 120590 =

0200Figure 6 and Table 2 illustrate the advantages of the M1

approach supposing a single assay with 120590 = 0100 two


0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

0806

0402

0

108

0604

020

11

09

07

05

03

01

F

Dt

0

02

04

06

08

1

002040608

112

R as

F d

ecre

ase

R as

F d

ecre

ase

R as

F d

ecre

ase

002040608

112

0 05 1 0 05 1D D

0

01

02

03

04

05

0 05 1t

010305070911

02 05 08 11

Pred

icte

d va

lues

Simulated values

0

02

04

0 025 05 075 1

Resid

uals

D

Bivariate approachConventional univariate approach

U2

U and B

B4

B3

B1

B2

0

02

04

06

08

1

0 05 1

Resp

onse

s

D

minus02

minus01

minus01

minus01minus04

U-t1 U-t2

U-t3 U-t4

U-t5 U-t6

m(E

D50)

Figure 6 Simulation (points) of a single assay (120590 = 0100 2 replicates no smoothing) and its fitting (lines) to models (1) (U series) and (7) (Bseries) In B series correlation between simulated and predicted results (B2) residuals as a function of the dose (B3) and dr relationships (Uand B) according to the univariate (dotted lines) and bivariate (solid line) approaches are also shown Acceptable fittings were not possible at1199051and 1199056(omitted points at 119905

6were located outside the represented domain) (The rest of keys as in Figure 2) See also text and Table 2

Table 2 Parametric estimates and confidence intervals (as of the estimate value) obtained by applying uni- and bivariate approaches (1)and (7) to the simulation of a single assay (120590 = 0100 two replicates no smoothing) Results at times 119905

1and 1199056did not allow acceptable fittings

and at 1199055the 119886 estimate was not significant (CI gt 100) See also Figure 8

True parametric valuesBivariate approach Uivariate approach at the specified times

Estim CI () 1199052

1199053

1199054

1199055

Estim CI () Estim CI () Estim CI () Estim CI ()120591 = 0600 0603 101 mdash mdash mdash mdash mdash mdash mdash mdashV = 2500 2635 134 mdash mdash mdash mdash mdash mdash mdash mdash119870 = 0800 0807 34 0774 173 0946 89 1000 146 0989 153119898 = 0250 0247 133 0451 163 0334 90 0231 208 0190 174119886 = 2000 1777 215 3127 536 4097 441 2689 723 5073 gt1001199032 0980 0980 0989 0962 0932


0

01

02

03

04

Freq

uenc

y

Freq

uenc

y

Freq

uenc

y

018 03 042 054m

13 33 53 73a

182 262 342 42205 06 070

01

02

03

04

Freq

uenc

y

0

01

02

03

04

Freq

uenc

y

07 09 11 130

01

02

03

0

01

02

03

04

0

01

02

03

0

01

02

03

04

0

01

02

03

K

120591

Figure 7 Distributions of the parametric estimates obtained with models (1) (white) and (7) (grey) in 2000 repetitions of an assay with120590 = 0100 2 replicates and smoothed data along the variable119863 Dotted lines indicate parametric true values

replicates and no smoothing Another comparison usingthe same error and selecting for M0 the time with the bestfit is that referring to the distributions of the parametricestimates supposing 2000 repetitions two replicates andsmoothing (Figure 7) Even so M0 produced strongly biasedand platykurtic distributions very problematic in practice

33 Smoothing The moving average method is recom-mended by some authors [24] to determinate accurately theED50

and indeed it reduces the effect of the experimentalerror giving statistical significance to estimates which wouldnot have it by using raw data The drawback is the biasthat this method produces in some parametric estimatesIn a Weibull function without error the usual smoothing(window = 3) causes bias only on the parameter 119886 reducingslightly the slope (an effect that is accentuated by higher order

windows) In the presence of error the situation becomesmore complex since smoothing tends to correct the slopeincrease statistically associatedwith the homoscedastic errorbut it is easy to realize that it can also lead to overestimate theasymptote if it is not properly defined by the experimentaldata (this problem is usually corrected by including therestriction119870 le 1 in the fitting algorithm although at the riskof biasing the parameters119898 and 119886)

A bivariate model as (7) admits smoothing along eitherof its two variables or even bothThe above described resultswere obtained by smoothing along the dose and as showsthe top part of Figure 5 the drawback was an admissibleunderestimation of the parameters V and 119886 Smoothingalong the time was less satisfactory for two reasons themoving averagemethod involved less values and a decreasingsigmoidmdashfirst equation of model (7)mdashproved to be more


sensitive than an increasing one to the homoscedastic error(we ignore the cause of this fact but it was repeatedlyconfirmed in series of 2000 runs with symmetrical curvesor not) In any case this treatment produced a strongbias in the parameter V (198 instead of 250) and weakerin 119886

When smoothing was applied along both variables (Fig-ure 5 down) the result showed a strong bias in V (theleast important parameter of the system) but in return itproduced even with 120590 = 0250 unbiased estimates forthe rest of the parameters all of them (including V) aresignificant in 100 of the repetitions This means that alltoxicological parameters as well as the sperm half-life canbe estimated with a reasonable accuracy even when thestandard deviation of the observations reaches 25 of theirmaximum value

34 Error and Experimental Effort It is pertinent to note thatthe conditions imposed to the described simulations werestricter than the real ones In practice the fertilization ratioat time zero is a unique value of the system independentof the dose and coded as 1 Thus no initial value can begreater than 1 and after a certain time especially in thepresence of toxic values 119865

119888119905gt 1 are in practice much less

probable than those due to a random normalmdashwith meanequal to 0ndashnumber generator Moreover although a value119865119888119905

gt 1198650119905mdashproducing a negative response 119877

119865mdashis possible

a value 119865119888119905

lt 0 is not In Figures 6(B1) and 6(B2) itcan be seen that a part of the accepted error correspondsto such cases (119865

1198880gt 1 and 119865

119888119905lt 0) If simulation

includes a condition converting these values into 0 and 1respectively the CI produced bymodel (7) without replicatesor smoothing are reduced 16ndash20 (the gain is lower inmodel(1)) This condition although may be more realistic wasnot used

On the other hand experimental evidence suggests thatthe real error in this assay is rather heteroscedastic andstronger in middle than in extreme observational valuesIrrespective of using ordinary or weighted least squaresas regression method this condition produces less drasticdeviations than those derived from the homoscedastic errorapplied here

In any case to achieve the precision obtained withmodel (7) without replicates using model (1)mdashnow ignoringits problematic interpretationmdashwould require at least 4-5replicates Thus a usual assay in the M0 approach with 8doses and 4 times would need at least 128 experimental unitsIn the M1 approach 8 times 7 = 56 units would produce at leastan equivalent precision and more information and even theuse of two replicates (112 units) would be more economicwith a much higher precision Moreover one additionaldose improves CI in both approaches but one additionaltime only does it in the case of M1 since in M0 it meansmerely to obtain a new and different DR profile Finally thesimpler protocol required by the M1 approach minimizes theoperative inaccuracies potentially affecting the independentvariables

4 Discussion

As a consequence of the drift with time produced by theM0 approach in a toxicological assessment the 119898

119865values

underestimate the toxic potency (regarding119898120591inM1) at short

times and overestimate it at longer timesThe opposite occursin the maximum response 119870

119865regarding 119870

120591 The statistically

most acceptable fittings are found in general at central timesbut even so the variations in the toxicological parameters aretoo wide the best fit is not necessarily themost representativeone and there is not a criterion to define a priori the mostappropriate time

On the other hand if the DR curves resulting from thetwo approaches are compared it can be stated that M0 tendsto underestimate the effects of low doses even when 119898

119865lt

119898120591at high times (Figure 6(U and B)) Although extremely

arguable two indexes very cited in the ecolegal field [31] areNOEC and LOEC (no observed and lowest observed effectconcentration resp) Both are obtained by variance analysisdefine essentially the limitations of this analysis as a methodof toxicological assessment and are definitely tending tounderestimate any toxic effect This will be underestimateda fortiori if NOEC and LOEC are based on theM0 approach

Even more controversial is the fact that the results of theM0 approach depend on the sperm half-life 120591 in the assayconditions (in fact half-life should be included among thestandardization needs forM0) Since temperature shortens 120591its effect (canceled in M1 by using half-life variations) takespart in M0 through the effect of 120591 on the fertilization ratioon which the assessment is based (Figure 8) This creates aninevitable and artifactual underestimation of the toxicity atlow temperatures beyond the result of a slower metabolismand a complementary overestimation at high temperaturesSince bioassays are usually carried out at temperatures closeto those characterizing the habitat of the wild animal theapplication of M0 will involve a higher legislative tolerancein cold than in warm seas

5 Conclusions

The bioassay studied here is of a special elegance and applica-bility which are lost to a great extent because of the use of thefertilization ratio as evaluation criterion The essence of thisissue is the fact that in a dynamic system any perturbationcannot be properly characterized through isolate values ofany nonlinear-in-time variable but through the variation ofsome parameter of a model including time in its structureThis conflict not too rare in physiological contexts is similarfor example to that one that arises when a toxic effect ona microbial or cellular batch culture is assessed by using avariable as biomass or some primary metabolite instead ofsome parameter of some growth equation

When this characteristic of the target system is not takeninto account the difficulty to obtain reproducible resultsoften leads to an accumulation of procedural restrictionswhich only overstandardize the protocol obstructing itsexecution without solving the main problem We believethat sperm bioassays are currently in this condition despitethe existence of very rigorous results about the fertilization


0

02

04

06

01 03 05 07

mF

t

Figure 8 Effect of the spermatic half-life (120591) on the estimation ofthe parameter 119898

119865(ED50) by means of model (1) at different times

supposing observations with a negligible error (120590 = 5 times 10minus4)

Simulations with model (7) combining the following pairs of trueparametric values ◻ 120591 = 06 119898

120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898

120591= 035 (the rest of the parametric

values as inTable 1) Bars indicate the confidence intervals (120572 = 005)of the estimates

kinetics and the factors affecting it which provide the keyto reformulate the toxicological focus in the form proposedhere

Focusing the bioassay on a parameter (the sperm half life)is necessary first of all if we want a toxicological assessmentwith a unique solution and a clear interpretation It is alsomore realistic since the exposure of the gametes to the toxicduring only a fraction of their life span has little to do withwhat occurs in natural conditions Finally the procedureis conceptually more direct experimentally simpler andmore robust against the observational error and variationsin the particular variables of the system and it removes theartifactual effect of temperature

Using a bivariate model can seem a disadvantage regard-ing other apparent simpler routines In this case however thecurrent informative means make its application trivial whilethe apparently simpler solution requires amore embarrassingprotocol and produces more problematic results DeLean etal [32] underlined time ago in a similar context to this theadvisability of ldquo analyzing all of the curves simultaneouslyforcing them to share certain parameters in commonrdquo Inagreementwith this opinion we believe [33ndash36] that bivariateapproaches of the type proposed here could improve anybioassay in which the inhibitory or stimulatory action of aneffector is superposed on the variation with time of the targetsystem or the particular time course of the response is arelevant aspect of that action Some bioassays that are basedon hemolytic processes could be examples on this matter

Finally from the ecotoxicological point of view it couldbe pointed out that in contrast to what seems an implicitassumption the sperm bioassays are not an alternative tolarval ones In fact the two types of results can be consideredonly as two components of the real impact of the toxic understudy on the target species Perhaps this type of assumptionsis part of the reasons explaining why the state of manyecosystems is more critical than which is supposed by theparsimony of the respective environment protection policies

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors express thanks to Ministerio de Ciencia eInnovacion (CTM2010-18411 FEDER funds from EuropeanUnion) for financial support Miguel Angel Prieto Lage wasawarded JAE-predoctoral contract by CSIC They want toexpress their gratitude to Araceli Menduina Santome andDiego Rial Conde for their technical work

References

[1] A P Negri and A J Heyward ldquoInhibition of coral fertilisationand larval metamorphosis by tributyltin and copperrdquo MarineEnvironmental Research vol 51 no 1 pp 17ndash27 2001

[2] Z-C Xie C W Nga P-Y Qian and J-W Qiu ldquoResponsesof polychaete Hydroides elegans life stages to copper stressrdquoMarine Ecology Progress Series vol 285 pp 89ndash96 2005

[3] L Hoadley ldquoCertain effects of the salts of the heavy metalson the fertilization reaction in Arbacia punctulatardquo BiologicalBulletin vol 44 pp 255ndash279 1923

[4] P A Dinnel Q J Stober and D H DiJulio ldquoSea urchin spermbioassay for sewage and chlorinated seawater and its relation tofish bioassaysrdquoMarine Environmental Research vol 5 no 1 pp29ndash39 1981

[5] P A Dinnel J M Link and Q J Stober ldquoImproved method-ology for a sea urchin sperm cell bioassay for marine watersrdquoArchives of Environmental Contamination and Toxicology vol16 no 1 pp 23ndash32 1987

[6] P A Dinnel J M Link Q J Stober M W Letourneau andW E Roberts ldquoComparative sensitivity of sea urchin spermbioassays to metals and pesticidesrdquo Archives of EnvironmentalContamination and Toxicology vol 18 no 5 pp 748ndash755 1989

[7] G Pagano A Esposito and G G Giordano ldquoFertilizationand larval development in sea urchins following exposure ofgametes and embryos to cadmiumrdquo Archives of EnvironmentalContamination and Toxicology vol 11 no 1 pp 47ndash55 1982

[8] G Pagano M Cipollaro G Corsale et al ldquoComparativetoxicities of benzene chlorobenzene and dichlorobenzenesto sea urchin embryos and spermrdquo Bulletin of EnvironmentalContamination and Toxicology vol 40 no 4 pp 481ndash488 1988

[9] G Pagano B Anselmi P A Dinnel et al ldquoEffects on seaurchin fertilization and embryogenesis of water and sedimentfrom two rivers in Campania Italyrdquo Archives of EnvironmentalContamination and Toxicology vol 25 no 1 pp 20ndash26 1993


[10] Environment Canada ldquoBiological test method fertilizationassay using echinoids (sea urchins and sand dollars) amendedNovember 1997rdquo North Vancouver BC Canada EPS 1RM271992

[11] S Lera and D Pellegrini ldquoEvaluation of the fertilizationcapability of Paracentrotus lividus sea urchin storaged gametesby the exposure to different aqueous matricesrdquo EnvironmentalMonitoring and Assessment vol 119 no 1ndash3 pp 1ndash13 2006

[12] A Fabbrocini M Di Stasio and R DrsquoAdamo ldquoComputerizedspermmotility analysis in toxicity bioassays a new approach topore water quality assessmentrdquo Ecotoxicology and Environmen-tal Safety vol 73 no 7 pp 1588ndash1595 2010

[13] M A Murado M P Gonzalez and J A Vazquez ldquoDose-response relationships an overview a generative model and itsapplication to the verification of descriptive modelsrdquo Enzymeand Microbial Technology vol 31 no 4 pp 439ndash455 2002

[14] M A Murado J A Vazquez D Rial and R Beiras ldquoDose-response modelling with two agents application to the bioassayof oil and shoreline cleaning agentsrdquo Journal of HazardousMaterials vol 185 no 2-3 pp 807ndash817 2011

[15] P Riobo B Paz J M Franco J A Vazquez andM A MuradoldquoProposal for a simple and sensitive haemolytic assay forpalytoxin Toxicological dynamics kinetics ouabain inhibitionand thermal stabilityrdquo Harmful Algae vol 7 no 4 pp 415ndash4292008

[16] P Riobo B Paz J M Franco J A Vazquez M A Murado andE Cacho ldquoMouse bioassay for palytoxin Specific symptomsand dose-response against dose-death time relationshipsrdquo Foodand Chemical Toxicology vol 46 no 8 pp 2639ndash2647 2008

[17] J A Vazquez M P Gonzalez and M A Murado ldquoEffectsof lactic acid bacteria cultures on pathogenic microbiota fromfishrdquo Aquaculture vol 245 no 1ndash4 pp 149ndash161 2005

[18] M A Murado and J A Vazquez ldquoThe notion of hormesisand the dose-response theory a unified approachrdquo Journal ofTheoretical Biology vol 244 no 3 pp 489ndash499 2007

[19] M A Murado and J A Vazquez ldquoBiphasic toxicodynamicfeatures of some antimicrobial agents on microbial growth adynamic mathematical model and its implications on horme-sisrdquo BMCMicrobiology vol 10 article 220 2010

[20] N Kobayashi ldquoComparative sensitivity of various developmen-tal stages of sea urchins to some chemicalsrdquoMarine Biology vol58 no 3 pp 163ndash171 1980

[21] D R Levitan M A Sewell and F-S C Fu-Shiang ChialdquoKinetics of fertilization in the sea urchin Strongylocentrotusfranciscanus interaction of gamete dilution age and contacttimerdquo Biological Bulletin vol 181 no 3 pp 371ndash378 1991

[22] A ANovelli C Losso P F Ghetti andAVGhirardini ldquoToxic-ity of heavy metals using sperm cell and embryo toxicity bioas-says with Paracentrotus lividus (Echinodermata Echinoidea)comparisons with exposure concentrations in the Lagoon ofVenice Italyrdquo Environmental Toxicology and Chemistry vol 22pp 1295ndash1301 2003

[23] S Lera S Macchia and D Pellegrini ldquoStandardizing themethodology of sperm cell test with Paracentrotus LividusrdquoEnvironmental Monitoring and Assessment vol 122 no 1ndash3 pp101ndash109 2006

[24] E Jonczyk K G Doe P C Wells and S G Yee ldquoTechnicalevaluation of the sea urchin fertilization test proceedings of aworkshop in Dartmouth Nova Scotiardquo in Proceedings of the17th Annual Aquatic Toxicity Workshop P Chapman F BishayE Power et al Eds vol 1 of Canadian Technical Report Of

Fisheries amp Aquatic Sciences no1774 pp 323ndash330 VancouverBC Canada 1991

[25] D J Marshall ldquoReliably estimating the effect of toxicants onfertilization success in marine broadcast spawnersrdquo MarinePollution Bulletin vol 52 no 7 pp 734ndash738 2006

[26] P R Krause ldquoEffects of an oil production effluent ongametogenesis and gamete performance in the purple seaurchin (Strongylocentrotus purpuratus stimpson)rdquo Environ-mental Toxicology and Chemistry vol 13 no 7 pp 1153ndash11611994

[27] H Vogel G Czihak P Chang and W Wolf ldquoFertilizationkinetics of sea urchin eggsrdquo Mathematical Biosciences vol 58no 2 pp 189ndash216 1982

[28] C A Styan andA J Butler ldquoFitting fertilisation kineticsmodelsfor free-spawning marine invertibratesrdquo Marine Biology vol137 no 5-6 pp 943ndash951 2000

[29] S Prikler ldquoRobert de Levie advanced Excel for scientific dataanalysis 2nd edrdquo Analytical and Bioanalytical Chemistry vol395 pp 1945ndash1964 2009

[30] G E P Box and M E Muller ldquoNote on the generation ofrandomnormal deviatesrdquoTheAnnals ofMathematical Statisticsvol 29 pp 610ndash611 1958

[31] M A Murado and M A Prieto ldquoNOEC and LOEC asmerely concessive expedients two unambiguous alternativesand some criteria to maximize the efficiency of dose-responseexperimental designsrdquo Science of the Total Environment vol461-462 pp 576ndash586 2013

[32] A DeLean P J Munson and D Rodbard ldquoSimultaneousanalysis of families of sigmoidal curves application to bioassayradioligand assay and physiological dose-response curvesrdquoTheAmerican journal of physiology vol 235 no 2 pp E97ndashE1021978

[33] M A Murado Garcia and M A Prieto Lage ldquoDose-responseanalysis in the joint action of two effectors A new approachto simulation identification and modelling of some basicinteractionsrdquo PLoS ONE vol 8 Article ID e61391 2013

[34] M A Prieto M A Murado J A Vazquez Y Anders andT P Curran ldquoA new microplate procedure for simultaneousassessment of lipophilic and hydrophilic antioxidants and pro-oxidants using crocin and 120573-carotene bleaching methods ina single combined assay tea extracts as a case studyrdquo FoodResearch International vol 53 pp 836ndash846 2013

[35] M A Prieto J A Vazquez and M A Murado ldquoComparisonof several mathematical models for describing the joint effectof temperature and ph on glucanex activityrdquo BiotechnologyProgress vol 28 no 2 pp 372ndash381 2012

[36] M A Prieto J A Vazquez and M A Murado ldquoHydrol-ysis optimization of mannan curdlan and cell walls fromEndomyces fibuliger grown in mussel processing wastewatersrdquoProcess Biochemistry vol 46 no 8 pp 1579ndash1588 2011

Submit your manuscripts athttpwwwhindawicom

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PeptidesInternational Journal of


Hindawi Publishing Corporation httpwwwhindawicom

International Journal of

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Zoology


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GenomicsInternational Journal of


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Advances in

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Nucleic AcidsJournal of

Volume 2014

Stem CellsInternational



Enzyme Research



Microbiology


2 Theoretical Background and Methods

21The Conventional Approach The current procedure withprecedents since almost one century ago [3] is a synthesisof those that were developed by Dinnel et al [4ndash6] andPagano et al [7ndash9] and it is recommended at presentby environmental agencies [10] The bioassay involves theexposure of a sperm suspension to increasing levels of atoxic agent during increasing times followed by the additionof an egg suspension to the treated sperm [11 12] Afterthe time required to reach the asymptotic maximum of thefertilization ratio in the absence of the agent (control) theproducts of the process are fixed with formalin and countedSubsequently the toxic effect of the increasing doses of theagent over the fertilization ratio is assessed through any dose-response (DR) model

Thus if1198650and119865119888are the fertilization ratios in the absence

of toxic (control) and at the toxic concentration (dose) 119888respectively the response quantified as 119877 = 1 minus (119865

1198881198650) can

be described with the Weibull dose-response model as anexample which is an especially versatile DR model [13ndash16]Using this equation in a reparametrized form [17ndash19] whichmakes it appropriate in this context we can write

119877 = 119870[1 minus exp(ln 05(119863119898)

119886

)] (1)

where119870 is the asymptotic maximum of 119877119863 the dose119898 thedose corresponding to half-maximum response (119898 = ED

50if

119870 = 1) and 119886 a shape parameter that defines (together with119870 and119898) the maximum slope of the function

It should be underlined that this assay solves elegantlyseveral key issues of the DR analysis (a) it works with alarge population a condition that is difficult to satisfy if thetarget species is not a microorganism (b) it deals with anontogenically essential and physiologically sensitive process(c) it is a fast test avoiding the changes in the physical-chemical system [5] or in the biotic sensitivity [20] which arepossible in longer assays such as those that are focused onlarval growth inhibitions Short times are specially interestingin the assessment of lipophilic toxics whose micelles cancoalesce during the course of static assays lasting a numberof hours causing uncertainty regarding the real dose in theimmediate environment of the organism

However the direct use of the drop in the fertilizationratio as response pays a steep price in practical complicationsand ambiguity of the results both because of the characteris-tics of the system and the structure of its formal treatment

211 Exigencies of the Biologic System Some necessary cau-tions in this regard are of a common kind in many analyticalmethods This is the case for example of the effects of statevariables as temperature and composition (essentially pHand salinity) or the need to use glass material [5] A factthat has also correlates in other methods is the requirementfor maximizing the sensitivity of a fertilization ratio forthe control close to 1 but less than 1 to avoid as much aspossible hiding the toxic effect by a possible excess of spermHowever in a more specific and obstructive way the assay

is affected by particular variables such as (1) the absoluteand relative gamete concentrations (2) the contact time (3)the sperm age (4) the dilution of the system accelerates theconsumption of its limited energy reserve probably due toan increase of respiration and therefore shorts out its lifespan The control of these last factors is difficult becausethe existence of interactions among them [21] preventsthe individualized selection of appropriate values In factstandardization is a customary claim in the bibliographyregarding this method [22ndash24] and other authors [25] evenhave argued the need to use more than one gamete ratio totake into account the reproductive failure due to polyspermy

212 Implications of the Descriptive Approach Under thispoint of view the method shows the following problematicaspects

(1) Although it is recognized that the exposure timeto toxic agent affects the fertilization ratio [5] thisvariable is not formally included into univariate DRmodels as (1) Therefore since each time leads toa different assessment the decision about which ismore representative is arbitrary

(2) The short life span of the gametes makes feasiblea more realistic assay in which the exposure timecover as their entire life period as it occurs in naturalconditionsThe use of briefer exposure times can onlycontribute to increase the error and underestimate thetoxic effect

(3) If the sum of the exposure and contact times does notexceed the sperm life span it could happen (assumingthat the toxic action reduces the sperm activity)that at the end point the fertilization processes areunder different doses at different distances fromtheir respective maxima making any comparisonquestionable

(4) The values of the fertilization ratio 119865 contain infor-mation regarding the effects of the toxic action andthe sperm age but the formal treatment ignores thesecond oneThus the variability linked to both effectsis accumulated only over the toxic action causingtwo undesirable consequences the inaccuracy of theresult and the bias of the parametric estimates

(5) Finally as we will see in the results section tem-perature exerts an inevitable and purely artefactualeffectmdashthat is apart from the one ruled by theArrhenius equationmdashin any assessment through theconventional method

22 Factual Frame of the Assay Fertilization Kinetics Inthe reproductive phenomenology of the sea urchin rich instudies the most of its quantitative behavior both in exper-imental [21] and observational [26] contexts is explained bya fertilization kinetic model which Vogel et al [27] calledmdashacurious tribute toMozartmdashDonOttavioThis model assumesthat the random encounter between gametes follows a secondorder kinetics in which the egg retains a certain number of


0

02

04

06

08

1

0 5 10 15 20

F

Time (min)

(a)

0 5 10 15 20Time (min)

0

02

04

06

08

1

F

(b)

0 5 10 15 200

02

04

06

08

1

F

Time (min)

(c)




minus6 1205730= 33 times 10


0 respectively


0and 119874

0being the


119865 (119905) = 1 minus expminus120573

1205730

1198780

1198740

[1 minus exp (minus12057301198740119905)] (2)



0) or effective (in



0= 11987801198740ratios which



0


0increases










0and 119865



0ratio (Figure 2




119865 = 119865119898exp(ln 05( 119905

120591)

V) (4)






1438

62

14003800

6200

1

08

06

04

02

0

F

S0O0

(a)

1

08

06

04

02

0

1438

62

14003800

6200

F

S0O0

(b)

1

08

06

04

02

00 4000 8000


F

at S0O0 = 100

(c)




Time (min)0

1

0

08

06

04

02

20 40 60

F (u

nits)


Time (units)

F (u

nits)

Time (units)

F (u

nits)

Finfin at age = 0

Finfin at age = t




119898= 1 and


119865 = exp [ln 05( 119905

120591)

V] (5)






119877120591= 1 minus

120591

1205910

therefore 120591 = 1205910(1 minus 119877

120591) (6)


119865 = exp [ln 05( 119905

120591)

V]


119898)

119886

)]

(7)















119894






0ratio However


0) 119865infin




0ratio











1)1(119899minus2) where 119909

1is the


119873 (0 120590) = 120590 [(minus2 ln 1199061)12

] sin (21205871199062) (8)

where 1199061and 119906










119865= 1 minus (119865

1198881199051198650119905) that is as the








1199052

1199053

1199054

1199055

1199056




119888119905)










0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

108

0604020

108

0604

020

1

08

06

04

02

0

F

Dt

0

02

04

06

08

1

0 05 1

F

t

0

02

04

06

08

1

0 05 1

R as

F d

ecre

ase

D

0

02

04

06

08

0 05 1t

Bivariate approach

0

02

04

06

08

1

0 02 04 06 08 1

R as

F d

ecre

ase

D


U1

U2

B1

B2

B3

B4

t1

t2

t3

t4t5

t6

t1

t2

t3t4

t5

t6

m (E

D50)







119865




004 008 012 0160

1

2

3

4

004 008 012 016

K m

and

a es

timat

es

K m

and

a es

timat

es

0

1

2

3

4

004 008 012 016 004 008 012 016





0

1

2

3

4

004 008 012 016 020 0240

1

2

3

4

004 008 012 016 020 024




120591an

d

estim

ates

120591an

d

estim

ates




3and 119905

4 By combining two









0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

0806

0402

0

108

0604

020

11

09

07

05

03

01

F

Dt

0

02

04

06

08

1

002040608

112

R as

F d

ecre

ase

R as

F d

ecre

ase

R as

F d

ecre

ase

002040608

112

0 05 1 0 05 1D D

0

01

02

03

04

05

0 05 1t

010305070911

02 05 08 11

Pred

icte

d va

lues

Simulated values

0

02

04

0 025 05 075 1

Resid

uals

D


U2

U and B

B4

B3

B1

B2

0

02

04

06

08

1

0 05 1

Resp

onse

s

D

minus02

minus01

minus01

minus01minus04

U-t1 U-t2

U-t3 U-t4

U-t5 U-t6

m(E

D50)







Estim CI () 1199052

1199053

1199054

1199055



0

01

02

03

04

Freq

uenc

y

Freq

uenc

y

Freq

uenc

y

018 03 042 054m

13 33 53 73a

182 262 342 42205 06 070

01

02

03

04

Freq

uenc

y

0

01

02

03

04

Freq

uenc

y

07 09 11 130

01

02

03

0

01

02

03

04

0

01

02

03

0

01

02

03

04

0

01

02

03

K

120591















a value 119865119888119905


1198880gt 1 and 119865





4 Discussion


119865values







119865lt




5 Conclusions




0

02

04

06

01 03 05 07

mF

t





120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898









Acknowledgments


References














































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


0

02

04

06

08

1

0 5 10 15 20

F

Time (min)

(a)

0 5 10 15 20Time (min)

0

02

04

06

08

1

F

(b)

0 5 10 15 200

02

04

06

08

1

F

Time (min)

(c)




minus6 1205730= 33 times 10


0 respectively


0and 119874

0being the


119865 (119905) = 1 minus expminus120573

1205730

1198780

1198740

[1 minus exp (minus12057301198740119905)] (2)



0) or effective (in



0= 11987801198740ratios which



0


0increases










0and 119865



0ratio (Figure 2




119865 = 119865119898exp(ln 05( 119905

120591)

V) (4)






1438

62

14003800

6200

1

08

06

04

02

0

F

S0O0

(a)

1

08

06

04

02

0

1438

62

14003800

6200

F

S0O0

(b)

1

08

06

04

02

00 4000 8000


F

at S0O0 = 100

(c)




Time (min)0

1

0

08

06

04

02

20 40 60

F (u

nits)


Time (units)

F (u

nits)

Time (units)

F (u

nits)

Finfin at age = 0

Finfin at age = t




119898= 1 and


119865 = exp [ln 05( 119905

120591)

V] (5)






119877120591= 1 minus

120591

1205910

therefore 120591 = 1205910(1 minus 119877

120591) (6)


119865 = exp [ln 05( 119905

120591)

V]


119898)

119886

)]

(7)















119894






0ratio However


0) 119865infin




0ratio











1)1(119899minus2) where 119909

1is the


119873 (0 120590) = 120590 [(minus2 ln 1199061)12

] sin (21205871199062) (8)

where 1199061and 119906










119865= 1 minus (119865

1198881199051198650119905) that is as the








1199052

1199053

1199054

1199055

1199056




119888119905)










0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

108

0604020

108

0604

020

1

08

06

04

02

0

F

Dt

0

02

04

06

08

1

0 05 1

F

t

0

02

04

06

08

1

0 05 1

R as

F d

ecre

ase

D

0

02

04

06

08

0 05 1t

Bivariate approach

0

02

04

06

08

1

0 02 04 06 08 1

R as

F d

ecre

ase

D


U1

U2

B1

B2

B3

B4

t1

t2

t3

t4t5

t6

t1

t2

t3t4

t5

t6

m (E

D50)







119865




004 008 012 0160

1

2

3

4

004 008 012 016

K m

and

a es

timat

es

K m

and

a es

timat

es

0

1

2

3

4

004 008 012 016 004 008 012 016





0

1

2

3

4

004 008 012 016 020 0240

1

2

3

4

004 008 012 016 020 024




120591an

d

estim

ates

120591an

d

estim

ates




3and 119905

4 By combining two









0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

0806

0402

0

108

0604

020

11

09

07

05

03

01

F

Dt

0

02

04

06

08

1

002040608

112

R as

F d

ecre

ase

R as

F d

ecre

ase

R as

F d

ecre

ase

002040608

112

0 05 1 0 05 1D D

0

01

02

03

04

05

0 05 1t

010305070911

02 05 08 11

Pred

icte

d va

lues

Simulated values

0

02

04

0 025 05 075 1

Resid

uals

D


U2

U and B

B4

B3

B1

B2

0

02

04

06

08

1

0 05 1

Resp

onse

s

D

minus02

minus01

minus01

minus01minus04

U-t1 U-t2

U-t3 U-t4

U-t5 U-t6

m(E

D50)







Estim CI () 1199052

1199053

1199054

1199055



0

01

02

03

04

Freq

uenc

y

Freq

uenc

y

Freq

uenc

y

018 03 042 054m

13 33 53 73a

182 262 342 42205 06 070

01

02

03

04

Freq

uenc

y

0

01

02

03

04

Freq

uenc

y

07 09 11 130

01

02

03

0

01

02

03

04

0

01

02

03

0

01

02

03

04

0

01

02

03

K

120591















a value 119865119888119905


1198880gt 1 and 119865





4 Discussion


119865values







119865lt




5 Conclusions




0

02

04

06

01 03 05 07

mF

t





120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898









Acknowledgments


References














































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


1438

62

14003800

6200

1

08

06

04

02

0

F

S0O0

(a)

1

08

06

04

02

0

1438

62

14003800

6200

F

S0O0

(b)

1

08

06

04

02

00 4000 8000


F

at S0O0 = 100

(c)




Time (min)0

1

0

08

06

04

02

20 40 60

F (u

nits)


Time (units)

F (u

nits)

Time (units)

F (u

nits)

Finfin at age = 0

Finfin at age = t




119898= 1 and


119865 = exp [ln 05( 119905

120591)

V] (5)






119877120591= 1 minus

120591

1205910

therefore 120591 = 1205910(1 minus 119877

120591) (6)


119865 = exp [ln 05( 119905

120591)

V]


119898)

119886

)]

(7)















119894






0ratio However


0) 119865infin




0ratio











1)1(119899minus2) where 119909

1is the


119873 (0 120590) = 120590 [(minus2 ln 1199061)12

] sin (21205871199062) (8)

where 1199061and 119906










119865= 1 minus (119865

1198881199051198650119905) that is as the








1199052

1199053

1199054

1199055

1199056




119888119905)










0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

108

0604020

108

0604

020

1

08

06

04

02

0

F

Dt

0

02

04

06

08

1

0 05 1

F

t

0

02

04

06

08

1

0 05 1

R as

F d

ecre

ase

D

0

02

04

06

08

0 05 1t

Bivariate approach

0

02

04

06

08

1

0 02 04 06 08 1

R as

F d

ecre

ase

D


U1

U2

B1

B2

B3

B4

t1

t2

t3

t4t5

t6

t1

t2

t3t4

t5

t6

m (E

D50)







119865




004 008 012 0160

1

2

3

4

004 008 012 016

K m

and

a es

timat

es

K m

and

a es

timat

es

0

1

2

3

4

004 008 012 016 004 008 012 016





0

1

2

3

4

004 008 012 016 020 0240

1

2

3

4

004 008 012 016 020 024




120591an

d

estim

ates

120591an

d

estim

ates




3and 119905

4 By combining two









0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

0806

0402

0

108

0604

020

11

09

07

05

03

01

F

Dt

0

02

04

06

08

1

002040608

112

R as

F d

ecre

ase

R as

F d

ecre

ase

R as

F d

ecre

ase

002040608

112

0 05 1 0 05 1D D

0

01

02

03

04

05

0 05 1t

010305070911

02 05 08 11

Pred

icte

d va

lues

Simulated values

0

02

04

0 025 05 075 1

Resid

uals

D


U2

U and B

B4

B3

B1

B2

0

02

04

06

08

1

0 05 1

Resp

onse

s

D

minus02

minus01

minus01

minus01minus04

U-t1 U-t2

U-t3 U-t4

U-t5 U-t6

m(E

D50)







Estim CI () 1199052

1199053

1199054

1199055



0

01

02

03

04

Freq

uenc

y

Freq

uenc

y

Freq

uenc

y

018 03 042 054m

13 33 53 73a

182 262 342 42205 06 070

01

02

03

04

Freq

uenc

y

0

01

02

03

04

Freq

uenc

y

07 09 11 130

01

02

03

0

01

02

03

04

0

01

02

03

0

01

02

03

04

0

01

02

03

K

120591















a value 119865119888119905


1198880gt 1 and 119865





4 Discussion


119865values







119865lt




5 Conclusions




0

02

04

06

01 03 05 07

mF

t





120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898









Acknowledgments


References














































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology







119894






0ratio However


0) 119865infin




0ratio











1)1(119899minus2) where 119909

1is the


119873 (0 120590) = 120590 [(minus2 ln 1199061)12

] sin (21205871199062) (8)

where 1199061and 119906










119865= 1 minus (119865

1198881199051198650119905) that is as the








1199052

1199053

1199054

1199055

1199056




119888119905)










0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

108

0604020

108

0604

020

1

08

06

04

02

0

F

Dt

0

02

04

06

08

1

0 05 1

F

t

0

02

04

06

08

1

0 05 1

R as

F d

ecre

ase

D

0

02

04

06

08

0 05 1t

Bivariate approach

0

02

04

06

08

1

0 02 04 06 08 1

R as

F d

ecre

ase

D


U1

U2

B1

B2

B3

B4

t1

t2

t3

t4t5

t6

t1

t2

t3t4

t5

t6

m (E

D50)







119865




004 008 012 0160

1

2

3

4

004 008 012 016

K m

and

a es

timat

es

K m

and

a es

timat

es

0

1

2

3

4

004 008 012 016 004 008 012 016





0

1

2

3

4

004 008 012 016 020 0240

1

2

3

4

004 008 012 016 020 024




120591an

d

estim

ates

120591an

d

estim

ates




3and 119905

4 By combining two









0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

0806

0402

0

108

0604

020

11

09

07

05

03

01

F

Dt

0

02

04

06

08

1

002040608

112

R as

F d

ecre

ase

R as

F d

ecre

ase

R as

F d

ecre

ase

002040608

112

0 05 1 0 05 1D D

0

01

02

03

04

05

0 05 1t

010305070911

02 05 08 11

Pred

icte

d va

lues

Simulated values

0

02

04

0 025 05 075 1

Resid

uals

D


U2

U and B

B4

B3

B1

B2

0

02

04

06

08

1

0 05 1

Resp

onse

s

D

minus02

minus01

minus01

minus01minus04

U-t1 U-t2

U-t3 U-t4

U-t5 U-t6

m(E

D50)







Estim CI () 1199052

1199053

1199054

1199055



0

01

02

03

04

Freq

uenc

y

Freq

uenc

y

Freq

uenc

y

018 03 042 054m

13 33 53 73a

182 262 342 42205 06 070

01

02

03

04

Freq

uenc

y

0

01

02

03

04

Freq

uenc

y

07 09 11 130

01

02

03

0

01

02

03

04

0

01

02

03

0

01

02

03

04

0

01

02

03

K

120591















a value 119865119888119905


1198880gt 1 and 119865





4 Discussion


119865values







119865lt




5 Conclusions




0

02

04

06

01 03 05 07

mF

t





120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898









Acknowledgments


References














































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology





1199052

1199053

1199054

1199055

1199056




119888119905)










0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

108

0604020

108

0604

020

1

08

06

04

02

0

F

Dt

0

02

04

06

08

1

0 05 1

F

t

0

02

04

06

08

1

0 05 1

R as

F d

ecre

ase

D

0

02

04

06

08

0 05 1t

Bivariate approach

0

02

04

06

08

1

0 02 04 06 08 1

R as

F d

ecre

ase

D


U1

U2

B1

B2

B3

B4

t1

t2

t3

t4t5

t6

t1

t2

t3t4

t5

t6

m (E

D50)







119865




004 008 012 0160

1

2

3

4

004 008 012 016

K m

and

a es

timat

es

K m

and

a es

timat

es

0

1

2

3

4

004 008 012 016 004 008 012 016





0

1

2

3

4

004 008 012 016 020 0240

1

2

3

4

004 008 012 016 020 024




120591an

d

estim

ates

120591an

d

estim

ates




3and 119905

4 By combining two









0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

0806

0402

0

108

0604

020

11

09

07

05

03

01

F

Dt

0

02

04

06

08

1

002040608

112

R as

F d

ecre

ase

R as

F d

ecre

ase

R as

F d

ecre

ase

002040608

112

0 05 1 0 05 1D D

0

01

02

03

04

05

0 05 1t

010305070911

02 05 08 11

Pred

icte

d va

lues

Simulated values

0

02

04

0 025 05 075 1

Resid

uals

D


U2

U and B

B4

B3

B1

B2

0

02

04

06

08

1

0 05 1

Resp

onse

s

D

minus02

minus01

minus01

minus01minus04

U-t1 U-t2

U-t3 U-t4

U-t5 U-t6

m(E

D50)







Estim CI () 1199052

1199053

1199054

1199055



0

01

02

03

04

Freq

uenc

y

Freq

uenc

y

Freq

uenc

y

018 03 042 054m

13 33 53 73a

182 262 342 42205 06 070

01

02

03

04

Freq

uenc

y

0

01

02

03

04

Freq

uenc

y

07 09 11 130

01

02

03

0

01

02

03

04

0

01

02

03

0

01

02

03

04

0

01

02

03

K

120591















a value 119865119888119905


1198880gt 1 and 119865





4 Discussion


119865values







119865lt




5 Conclusions




0

02

04

06

01 03 05 07

mF

t





120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898









Acknowledgments


References














































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

108

0604020

108

0604

020

1

08

06

04

02

0

F

Dt

0

02

04

06

08

1

0 05 1

F

t

0

02

04

06

08

1

0 05 1

R as

F d

ecre

ase

D

0

02

04

06

08

0 05 1t

Bivariate approach

0

02

04

06

08

1

0 02 04 06 08 1

R as

F d

ecre

ase

D


U1

U2

B1

B2

B3

B4

t1

t2

t3

t4t5

t6

t1

t2

t3t4

t5

t6

m (E

D50)







119865




004 008 012 0160

1

2

3

4

004 008 012 016

K m

and

a es

timat

es

K m

and

a es

timat

es

0

1

2

3

4

004 008 012 016 004 008 012 016





0

1

2

3

4

004 008 012 016 020 0240

1

2

3

4

004 008 012 016 020 024




120591an

d

estim

ates

120591an

d

estim

ates




3and 119905

4 By combining two









0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

0806

0402

0

108

0604

020

11

09

07

05

03

01

F

Dt

0

02

04

06

08

1

002040608

112

R as

F d

ecre

ase

R as

F d

ecre

ase

R as

F d

ecre

ase

002040608

112

0 05 1 0 05 1D D

0

01

02

03

04

05

0 05 1t

010305070911

02 05 08 11

Pred

icte

d va

lues

Simulated values

0

02

04

0 025 05 075 1

Resid

uals

D


U2

U and B

B4

B3

B1

B2

0

02

04

06

08

1

0 05 1

Resp

onse

s

D

minus02

minus01

minus01

minus01minus04

U-t1 U-t2

U-t3 U-t4

U-t5 U-t6

m(E

D50)







Estim CI () 1199052

1199053

1199054

1199055



0

01

02

03

04

Freq

uenc

y

Freq

uenc

y

Freq

uenc

y

018 03 042 054m

13 33 53 73a

182 262 342 42205 06 070

01

02

03

04

Freq

uenc

y

0

01

02

03

04

Freq

uenc

y

07 09 11 130

01

02

03

0

01

02

03

04

0

01

02

03

0

01

02

03

04

0

01

02

03

K

120591















a value 119865119888119905


1198880gt 1 and 119865





4 Discussion


119865values







119865lt




5 Conclusions




0

02

04

06

01 03 05 07

mF

t





120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898









Acknowledgments


References














































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


004 008 012 0160

1

2

3

4

004 008 012 016

K m

and

a es

timat

es

K m

and

a es

timat

es

0

1

2

3

4

004 008 012 016 004 008 012 016





0

1

2

3

4

004 008 012 016 020 0240

1

2

3

4

004 008 012 016 020 024




120591an

d

estim

ates

120591an

d

estim

ates




3and 119905

4 By combining two









0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

0806

0402

0

108

0604

020

11

09

07

05

03

01

F

Dt

0

02

04

06

08

1

002040608

112

R as

F d

ecre

ase

R as

F d

ecre

ase

R as

F d

ecre

ase

002040608

112

0 05 1 0 05 1D D

0

01

02

03

04

05

0 05 1t

010305070911

02 05 08 11

Pred

icte

d va

lues

Simulated values

0

02

04

0 025 05 075 1

Resid

uals

D


U2

U and B

B4

B3

B1

B2

0

02

04

06

08

1

0 05 1

Resp

onse

s

D

minus02

minus01

minus01

minus01minus04

U-t1 U-t2

U-t3 U-t4

U-t5 U-t6

m(E

D50)







Estim CI () 1199052

1199053

1199054

1199055



0

01

02

03

04

Freq

uenc

y

Freq

uenc

y

Freq

uenc

y

018 03 042 054m

13 33 53 73a

182 262 342 42205 06 070

01

02

03

04

Freq

uenc

y

0

01

02

03

04

Freq

uenc

y

07 09 11 130

01

02

03

0

01

02

03

04

0

01

02

03

0

01

02

03

04

0

01

02

03

K

120591















a value 119865119888119905


1198880gt 1 and 119865





4 Discussion


119865values







119865lt




5 Conclusions




0

02

04

06

01 03 05 07

mF

t





120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898









Acknowledgments


References














































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


0

02

04

06

08

1

0 05 1

R as

hal

f-life

dec

reas

e

D

0806

0402

0

108

0604

020

11

09

07

05

03

01

F

Dt

0

02

04

06

08

1

002040608

112

R as

F d

ecre

ase

R as

F d

ecre

ase

R as

F d

ecre

ase

002040608

112

0 05 1 0 05 1D D

0

01

02

03

04

05

0 05 1t

010305070911

02 05 08 11

Pred

icte

d va

lues

Simulated values

0

02

04

0 025 05 075 1

Resid

uals

D


U2

U and B

B4

B3

B1

B2

0

02

04

06

08

1

0 05 1

Resp

onse

s

D

minus02

minus01

minus01

minus01minus04

U-t1 U-t2

U-t3 U-t4

U-t5 U-t6

m(E

D50)







Estim CI () 1199052

1199053

1199054

1199055



0

01

02

03

04

Freq

uenc

y

Freq

uenc

y

Freq

uenc

y

018 03 042 054m

13 33 53 73a

182 262 342 42205 06 070

01

02

03

04

Freq

uenc

y

0

01

02

03

04

Freq

uenc

y

07 09 11 130

01

02

03

0

01

02

03

04

0

01

02

03

0

01

02

03

04

0

01

02

03

K

120591















a value 119865119888119905


1198880gt 1 and 119865





4 Discussion


119865values







119865lt




5 Conclusions




0

02

04

06

01 03 05 07

mF

t





120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898









Acknowledgments


References














































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


0

01

02

03

04

Freq

uenc

y

Freq

uenc

y

Freq

uenc

y

018 03 042 054m

13 33 53 73a

182 262 342 42205 06 070

01

02

03

04

Freq

uenc

y

0

01

02

03

04

Freq

uenc

y

07 09 11 130

01

02

03

0

01

02

03

04

0

01

02

03

0

01

02

03

04

0

01

02

03

K

120591















a value 119865119888119905


1198880gt 1 and 119865





4 Discussion


119865values







119865lt




5 Conclusions




0

02

04

06

01 03 05 07

mF

t





120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898









Acknowledgments


References














































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology









a value 119865119888119905


1198880gt 1 and 119865





4 Discussion


119865values







119865lt




5 Conclusions




0

02

04

06

01 03 05 07

mF

t





120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898









Acknowledgments


References














































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


0

02

04

06

01 03 05 07

mF

t





120591= 025 ◼ 120591 = 06 119898

120591= 035 ⃝

120591 = 04119898120591= 025 e 120591 = 06119898









Acknowledgments


References














































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology





































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology








Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

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