Extension of the biotic ligand model of acute toxicity to a ...

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Extension of the biotic ligand model of acute toxicity to a ...

310 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343metals, species sensitivity and others, where theSBM may also be ofpractical utility. More generally,it is envisioned that the approach may alsohave much broader utility, as the specialized applicationfor sodium that is described herein is adaptedfor use in the context of the considerably moregeneralized IBM framework, a framework thatwould be ofuse in the study ofa wide variety ofphysiological and toxicological processes.2. Description of the sodium balance modelframeworkA fundamental premise of the BLM of acutetoxicity is that, regardless ofthe site-specific waterchemistry and the magnitude ofthe 96-h LC50,which vary markedly with water chemistry, theLC50 is associated with a fixed level of accumulationat the biotic ligand (i.e. the LA50 is constant).For example, the 96-h LA50 for rainbowtrout has been estimated to be 17 nmolAgygramwet weight ofgill (17 nmolyg w; Paquin et al.,1999), and when the predicted Ag accumulationlevel equals this amount, the dissolved Ag concentrationshould correspond to the LC50, regardlessofthe other characteristics ofthe exposure water.It should be understood that, in the strictest sense,the LA50 is not simply the total accumulation ofmetal at the gill, but more specifically, it isintended to be the metal associated with thephysiologically active sites that affect the processesofinterest, iono- and osmoregulation. Thus, measurementofgill metal accumulation does not necessarilyprovide a direct measure ofthe quantityofinterest, although they may be related, andperhaps proportional to each other.As indicated previously on the left side of Fig.2q q1, in the context ofthe BLM, Ca , Na andqH are simply viewed as competing cations withrespect to the binding ofsilver at the biotic ligand.However, in the context ofthe SBM, it is recognizedthat there are other more direct effects ofthese cations on the organism itself, effects thatare important even in the absence ofexposure toa metal such as silver. In this regard, the subsequentdiscussion will focus on the interactions ofthese cations at the gill, as they pertain to thephysiological status ofthe organism, includingboth ionoregulatory and, to a lesser degree, osmoregulatoryprocesses (Fig. 1). In fact, for purposesofthis description ofthe SBM, the BLM itselfwill be described only briefly and the focus willshift from the ‘chemistry-based side’ of the bioticligand, shown to the left, to the ‘physiology-basedside’ ofthe biotic ligand, shown to the right. Thisis an area that has previously received only limitedattention in the context ofthe BLM. Specifically,as its name implies, the SBM will consider a massbalance ofsodium around the organism itself. Themass balance will provide a way to evaluate thechanges in sodium that occur over time in responseto the chemistry ofthe water, including the concentrationofsilver, the metal ofinterest herein.Although it is expected that many ofthe conceptualideas to be presented will generally apply notonly to fish, but to essentially all other forms ofaquatic life (Potts and Parry, 1964; Potts, 1994),ofparticular interest here are rainbow trout(Oncorhynchus mykiss).The right side ofFig. 1 illustrates the principalroutes ofuptake and loss ofsodium in freshwaterfish generally and rainbow trout in particular. Theimportant fluxes include the energy-requiringactive sodium uptake or influx at the gill (J ), ipassive diffusive loss or efflux at the gill (J ), and erenal excretion (J ), urinary losses associated withrthe filtration of blood by the kidney. Althoughthese renal losses are ofrelatively minor importancein the overall sodium balance, representingon the order of10% or less ofthe uptake rate ofsodium at the gill (Wood, 1989; Curtis and Wood,1991; Wood, 1992), they are of sufficient magnitudeto be included in the model. Similar conclusionshave been drawn for some invertebrates aswell. At the same time, inclusion ofrenal lossesserves to maintain a more general modeling frameworkfor analysis purposes. Although other sourcesand sinks ofsodium could readily be incorporatedinto the analysis, including uptake from drinkingwater (important in marine fish), transfer acrossthe skin and dietary intake, they will be neglectedfor purposes of the analyses to be presented herein.With regard to the dietary source, while not importantin short-term acute toxicity studies where thefish are not fed, such as the studies to be analyzedsubsequently, it may in fact be important in longertermchronic toxicity studies. The reason is thatdietary sodium intake may account for approximately25% ofthe total sodium intake duringchronic exposures and during periods ofionoregulatorystress, fish may quite literally eat theirway out oftrouble (D’Cruz and Wood, 1998).


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–3433112.1. Effect of water chemistry on ionoregulationThe mechanisms of uptake and efflux that affectthe whole body transfer of ions, especially transfersat the gill, have been studied extensively and willnot be gone into in detail here (see Hoar andRandall, 1984; Wood and Shuttleworth, 1995, fordetailed descriptions). Rather, we will focus onthe principal factors that affect the more limitedsubject of the sodium balance for fish. A fundamentalunderlying principle in this regard is thatunder normal, long-term average conditions, whenthe ambient water quality characteristics are relativelyuniform over time, the rates of active sodiumuptake and the sum of passive diffusion lossesplus renal losses ofsodium are in balance. Theresult is that the overall net uptake rate ofsodiumby the fish is approximately zero and a nearlyconstant plasma sodium level is maintained.Three ofthe cations that are included in variousversions ofthe BLM as competing cations, oneswhich reduce metal availability to the organism bycompeting with it for binding at the site of actionq 2q qoftoxicity, are H , Ca and Na . Although notthe only ions ofimportance with regard to ionoregulationby aquatic life, generally, these samethree cations are also ofsignificant physiologicalimportance to aquatic life with regard to Na qregulation. It is for this reason that they need tobe considered in the context ofthe SBM. Additionally,it is also necessary to understand theeffect of the metal stressor itself, how it relates tothe uptake and efflux of sodium to complete thedescription. While it will not be possible here tooutline all that is known in regard to these interactions,the essence ofthese interactions as theyare currently incorporated in the SBM will bedescribed.2.1.1. Direct effects of pH on ionoregulationThe pH ofthe ambient water, while not one ofthe controlling variables with regard to the datasetsto be presented subsequently, is still important ina more general sense and so it will be discussedbriefly here in regard to how it affects sodiumtransport. The balance of sodium is affected bypH in several ways. First, in a process that remainssomewhat controversial among scientists today, itqis commonly believed that Na is taken up byqaquatic organisms in exchange for H (alternaqtively or along with NH4as well) via a mecha-nism that is often referred to as the ‘proton-pump’hypothesis (Krogh, 1938; Kirschner, 1979; Potts,1994). This process allows the organism to maintainacidybase homeostasis in its internal fluidsand to satisfy the requirement of electro-neutrality.As a consequence ofthe fact that this exchangeoccurs, the pH ofthe external water (i.e. theqexternal concentration ofH ) will affect the dif-qfusion gradient of H between the ambient waterand the blood. This is expected to have a significanteffect on the magnitude of the H efflux, andqqhence the Na influx, to which it is tied. (It isnoteworthy to consider in this regard that Kirschner(1988), working with isolated frog skin,has shown that the apparent saturation ofNa qinflux described subsequently is caused by theqlimiting efflux of the H counterion.) A secondimportant effect of pH is that acidic pH conditionscan also lead to an increase in gill permeability orleakiness, thereby increasing diffusive losses ofsodium and other ions from the gill (Milligan andWood, 1982; McDonald, 1983a,b). Because pHlevels in the tests to be considered were circumneutraland relatively constant, neither oftheseinteractions will be considered further. However,they should be recognized as being ofpotentialimportance in some situations, considered at leastin a qualitative sense when attempting to interpretexperimental data, and as being areas where futuremodel development refinements would be of use.Given the present limitations in understanding ofthe precise mechanism ofhow this occurs, thedetails ofhow to formulate this process remain tobe worked out (Potts, 1994; Perry, 1997). Finally,Playle and Wood (1989a,b, 1991) in working withaluminum, have demonstrated the importance ofconsidering the shift in pH of the inspired water,which occurs in the gill boundary, on Al speciationin the gill micro-environment. This effect on pHmay also warrant further refinement in futureimplementations ofthe BLM and related models.2.1.2. Direct effects of calcium on ionoregulationq2qAs in the case ofH , the calcium ion, Ca , isalso included in the BLM as a cation that competeswith the trace metal ofconcern for binding at the2qbiotic ligand. However, Ca also has another,more direct effect on the physiology of the fish.Specifically, it has a direct effect on the ionicpermeability ofthe gill, that is, on the leakinessof the gill in regard to the diffusive transfer ofions. Simply, the paracellular junctions at the gillare composed ofa calcareous material, and it is


312 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343Fig. 2. An example ofthe sodium uptake kinetics for rainbow trout and the manner in which sodium uptake is inhibited by silver (datafrom Morgan et al., 1997). Note how J , the maximum uptake rate, is inhibited, rather than K the halfsaturation constant.M M,the tightness ofthese junctions, a characteristicthat controls the rate of diffusive transfer of neutralspecies and charged ionic species through them,2qthat is affected by the concentration of Ca inthe external water. This in turn has a direct effecton the rate ofloss ofions such as sodium by fish2q(i.e. it has an effect on J e). The effect of Ca ongill permeability will therefore be considered inthe analyses below.2.1.3. Direct effects of sodium on ionoregulationFinally, and perhaps most importantly, the concentrationofsodium in the external water needsq 2q qto be considered. As with H and Ca , Na haspreviously been considered in the BLM withregard to cationic competition between it and theionic form ofthe metal ofinterest for binding atthe biotic ligand. Hence the more sodium that ispresent, the lower the degree ofinteraction ofthemetal at the biotic ligand, and the level oftoxicityis thereby reduced. However, even in the absenceofthe metal being present, the concentration ofsodium in the external water is known to have adirect effect on the ability of the organism to takeup and regulate internal sodium levels. This effectofsodium is illustrated quite clearly by the dataofFig. 2 (Morgan et al., 1997). As shown hereby the filled dots and upper solid curve, the uptakeof sodium from the external water conforms to aMichaelis–Menten relationship (Michaelis andMenten, 1913):wxJ sJ C yŽ C qK .(1)i M w w Mwhere J is the sodium influx rate, adjusted for theiconcentration ofsodium, C , in the ambient water,wJMis the maximum sodium uptake rate and KMisthe halfsaturation concentration for sodium uptake(the concentration ofsodium in the external waterwhere the uptake is 50% of J ). The analysis ofMthese data yielded values ofthe Michaelis–Mentenkinetic parameters ("S.E.M.) of J s14.7"2.90Mmmolykg offish wet weight per day (mmolykg y wd) and K s0.257"0.090 mM. Ofparticular inter-Mest with regard to these results is that, over a rangeofrepresentative naturally occurring sodium levels,a decrease in the external sodium concentration isassociated with a decrease in the sodium uptakerate. As an example, based on these data, rainbowtrout exposed to an external sodium concentrationof0.50 mM will take up sodium at 8.4 mmolykg yd. However, ifthe sodium in the externalwwater is decreased to approximately 0.15 mM, theuptake rate will be reduced by about a factor of 2.The resulting imbalance is similar in degree to that


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343313which, ifcaused by a metal, could result insignificant adverse effects to the organism.Although internal systemic compensatoryresponses would be stimulated by these conditions,over the short-term at least, a fish that was subjectedto these conditions would be placed at adistinct ionoregulatory disadvantage at this reducedsodium level, particularly ifthis happened in associationwith exposure to a metal that adverselyaffects ionoregulation. This difference highlightswhy it is important to consider the effect of theconcentration ofsodium in the external water onqthe Na uptake process itself, not just the effectofmetal accumulation at the site ofaction oftoxicity on sodium uptake, or ofthe competitiveqeffect of Na on accumulation of the metal at thesite ofaction.2.1.4. Direct effects of metal concentration onionoregulationThe BLM ofacute toxicity, as previously proposedfor silver, copper, zinc and other metals,provides a way to predict the dissolved metalconcentration that will be associated with a fixedeffect, such as lethality, given the water qualitycharacteristics for the site of interest. A fundamentalpremise ofthe BLM is that the metal accumulationat the site ofaction oftoxicity that isassociated with the fixed effect is always the same.Further, it is implicitly assumed that the rate atwhich the damage to the organism accumulates,and hence the time that is required for the resultingeffect to be manifested, is also fixed. That is, thepredictions are associated with a fixed exposureduration. All that is required to predict an LC50for a given set of water quality characteristics anda fixed exposure duration is that the end-point ofinterest be related to a fixed LA50. However, ifthe objective is to evaluate the effect levels of ametal for different exposure durations, or for asituation where the metal concentration or otherwater quality characteristics vary over time, inboth magnitude and duration, then a more fundamentalrepresentation ofthe underlying processesis required. That is, it becomes necessary to understandand be able to define the details of the onewayion fluxes. This is because the degree of theimpairment (e.g. the degree ofinhibition ofthesodium uptake rate in the case ofcopper andsilver) will vary as the time for the end-point tobe manifested varies. What is required in thisinstance is a way to evaluate the one-way fluxessuch that it is possible to keep track ofthecumulative damage to the organism.As discussed previously, the lethality that resultsfrom elevated levels of metals such as silver andcopper is related to, at least in part, the inhibitionofthe sodium uptake process. The upper set ofdata presented previously on Fig. 2, which showedthe effect of external sodium levels on sodiumuptake, are compared to a second set ofresultsobtained at 2 mgyl silver to illustrate how exposureto silver interferes with the kinetics of this uptakeprocess (dashed curve, unfilled data points). Asshown, when 2 mgyl ofsilver is added to thewater for 48 h, the curve defining the sodiumuptake kinetics is reduced in magnitude to approximately50% ofthe upper curve, which wasobtained in the absence ofsilver. Analysis ofthese data yields a value of J s9.55"3.02Mmmolykg yd that was significantly lower than thewvalue for the control, while the value of K s M0.328"0.126 mM did not differ significantly fromthe control (Morgan et al., 1997). The interpretationofthese results by Morgan et al. was that theaddition ofsilver reduces the capacity, and hencethe maximum uptake rate, ofthe transport system,but not the affinity of the carrier, for sodium. Forthe example ofFig. 2, 2 mgyl ofsilver resulted inapproximately a 50% inhibition of J M. It is importantto recognize that a decrease in J is directlyreflected in J i, which varies also with the sodiumconcentration in the water, via Eq. (1), as thisrelationship will be incorporated in the computationsto be presented.The inhibition of JMis understood to be relatedto accumulation ofsilver at the biotic ligand, ormore specifically, its interaction with NKA.Although the level ofsilver accumulation at thefish gill is a measurable quantity, and while it maybe related to the level ofaccumulation at the actualbiotic ligand, a direct measurement ofthe latter(i.e. the level ofBL:Ag) is not readily made. Thisis in part because the principal cells ofthe gillthat are involved in sodium transport, the mitochondria-richchloride cells where much oftheNKA resides (most cells contain some NKA),represent only a small fraction (-10%) ofthetotal number ofgill cells (Perry, 1997). Silver maybind to sites associated with any ofthese cells,regardless ofwhether or not they are ofphysiologicalsignificance. In view of this, establishment ofa definitive relationship between the degree ofinhibition ofsodium uptake (i.e. a decrease in J iM


314 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343qat a given wNa x occurs via a decrease in J M) andthe level of Ag–NKA accumulation is difficult toachieve on the basis ofanalytical measurements.Even so, the available evidence indicates that theyare related in a dose-dependent manner and thatthis inhibition occurs rapidly yet is also reversible(e.g. Morgan et al., 1997; Bury et al., 1999a;Hussain et al., 1994). In view ofthese results theinhibition of JMwill be expressed in terms ofasigmoidal dose–response relationship given by:J sJ yµ 1qe ∂ (2)U w ( ln ( BL:Ag ) yln ( EC50 )) ybxM MHere, J * is the inhibited maximum sodiumMuptake rate and the EC50 (nmolyg ) for sodiumwuptake inhibition and b, the slope ofthe dose–response, will be evaluated by calibration to plasmasodium time series data in conjunction withthe BLM-predicted BL:Ag (nmolyg ) concentrawtion that is associated with each ofthe experimentaltreatments. Note that the version ofthe AgBLM that was used to predict the BL:Ag concentrationsin the analyses described herein (Paquinet al., 1999) is in the process ofbeing refined byongoing calibration efforts with recently obtaineddata. As such, the emphasis here is directed to theutility ofthe general approach and IBM frameworkthat are proposed, more than on use ofa particularversion ofthe BLM or SBM that is employedherein, as the latter are fully expected to continueto evolve and improve over time.2.2. Structure and formulation of the ion balancemodel for sodiumThe proposed model framework is viewed asbeing generally applicable, with the incorporationof appropriate modifications, to both fresh andmarine waters, and to both fish and invertebrates.While these other applications would require theinclusion ofthe appropriate source and sink termsfor sodium uptake (e.g. uptake within the gut andrepresentation ofthe gastro-intestinal tract as anadditional site ofaction oftoxicity), and recognitionthat the diffusive fluxes and active transportterms may reverse direction, the conceptualapproach should be valid. However, efforts to datehave focused on the development of a frameworkfor use with fish, rainbow trout in particular, in afreshwater setting. The model is formulated interms ofthe controlling mass balance equationsfor sodium about the fluid compartment volumesthat are represented. These differential equationsare solved numerically for the purpose of evaluatingthe effects of changes in relevant modelvariables on the concentrations ofthe respectiveinternal sodium pools over time. This sectiondescribes the model structure and the governingequations. For ease ofreference and comparison,the notation and units that are used, as well as theparameter values assigned in the modeling analysesofthe three main datasets to be discussed, aresummarized in Table 1.2.2.1. Representation of the internal fluidcompartmentsOfinterest is the regulation oflevels ofdissolvedions, sodium in particular, in the internalfluid compartments of a fish. There are a numberofways to configure these compartments and torepresent the exchanges that take place betweenthem (e.g. Nichols, 1987 describes six variations).The conceptual representation employed hereinconsists of four distinct fluid compartments (Fig.3). The vascular system is represented in terms ofa primary and secondary system, consistent withrelatively recent observations ofthe vascular systemofthe glass catfish (Steffenson and Lomholt,1992; Fig. 3a). Additionally, interstitial and intracellularfluid compartments are also considered,consistent with the conventional manner in whichthe fluid volumes in fish are reported (e.g. Holmesand Donaldson, 1969; Olson, 1992). The structureofthese interacting fluid compartments and themass transfers of sodium that are considered in themodel are illustrated on Fig. 3b. The physiologicalrepresentation is as follows. The gill is the organthat is primarily responsible for ionoregulation.The branchial epithelium ofthe gill, consists ofrelatively large chloride cells that control the activeuptake ofsodium from the water. The paracellularjunctions between the cells ofthe gill are wheremass transfer of sodium by passive diffusionoccurs (i.e. net diffusive losses in fresh water andnet gains in salt water). Although somewhat ofanoversimplification, NKA is primarily located atthe basolateral or plasma side ofthe chloride cell,and it is inhibition ofNKA activity by silver thatleads to a decrease in the active uptake ofsodiumfrom the water and an imbalance in whole bodysodium fluxes. This leads to a net rate of loss ofsodium from the fish and subsequent declines ofinternal levels ofsodium.Fig. 3b illustrates how the gill is positioned inrelation to the principal fluid compartments of a


Table 1Notation and parameter values used in IBM for sodiumParameter symbol Units Description Indicator Plasma Na Survival timedilution studies simulations simulationsSodium uptake kinetic parametersJ MmmolykgwydMaximum Na uptake rate 0 12.0 12.0J M*mmolykgwydMaximum Na uptake rate NA *** ***adjusted for Ag inhibition of J MJ immolykgwydActive Na uptake rate NA *** ***sJMfNasJMw(Cwy(CwqK M)xK M mM Halfsaturation constant for 0 0.040 0.050Na uptake at gillJ eJ rw f sC y(C qK )xNa w w MmmolykgwydPassive Na gill efflux NA *** ***mmolykgwydPassive Na renal efflux NA *** ***Fluid compartment volumesV 1 lykg w Primary intravascular fluid 0.023 0.023 0.023volume, IVFV 1V 2 lykg w Secondary intravascular fluid 0.048 0.048 0.048volume, IVFV 2V IS lykg w Interstitial fluid volume, ISFV 0.099 0.099 0.099V IC lykg w Intracellular fluid volume, ICFV Nil 0.160 0.160V EC lykg w Extracellular fluid volume, ECFV 0.170 0.170 0.170V Na lykg w Sodium space (sexchangeable NA 0.330 0.330Na poolyC 1 )Fluid compartment sodium concentrationsC w mM External water Na concentration 0 0.040 0.050C ic mM Na concentration initial condition, (100%) 137–139 140C i(ts0), in compartment iCiyCj mM Inter-compartmental *** *** ***Na concentration differenceC 1 mM Primary vascular system plasma *** *** ***Na concentrationC 2 mM Secondary vascular system *** *** ***plasma Na concentrationC IS mM Interstitial fluid volume Na *** *** ***concentrationC IC mM Intracellular fluid volume Na *** *** ***concentrationP.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343315


Table 1 (Continued)Parameter symbol Units Description Indicator Plasma Na Survival timedilution studies simulations simulationsPermeability coefficientsP GolykgwydGill permeability ofcontrol fish 0.036 0.0388–0.0394 0.0386P GlykgwydGill permeability oftreatment *** *** ***(exposed) fish, PGs fPGPGof PG – Gill permeability factor; NA NA ***q b 2q cf PGsawAg xwCa xA – Lead coefficient in expression for NA NAy43.09=10 (or 4.54)f PG for Ag in mgyl (or mM) unitsB –q bExponent for wAg x in expressionNA NA 2.05qfor f PG,Ag (units depend on a)C –2q cExponent for wCa x inNA NA y0.222qexpression for f PG,Ca inmMP ijlykgwydInter-compartmental permeabilitycoefficient for compartments i and jP 1,ISlykgwydPermeability between primary 0.10 0.10 0.10vascular system and ISFVP 2,ISlykgwydPermeability between secondary 0.10 0.10 0.10vascular system and ISFVP IS,IClykgwydPermeability between ISFV 0 0.10 0.10and ICFVP rlykgwydRenal loss rate permeability; set NA a ato achieve Jrs10% of JINQ 12lykgwydPrimary to secondary plasma 0.159 0.159 0.159IPClykg yd wskimming flow rateInter-compartmental permeabilitycoefficient (i.e. P i,j)Sodium uptake inhibition dose–response parametersAg mgyl Dissolved silver in exposure 0.0 ;3.2 ;100waterBL:Ag nmolyg w Biotic ligand silver, calculated NA 0–12 Ca tests: 30.9–32.1with the BLM Cl tests: 6.83–32.1EC50 nmolyg w BL:Ag associated with the 50% NA 15.8 15.8b Slope ofdose–response curve NA 0.278 0.278for JMinhibitions f (BL:Ag)effect levela, Set to achieve Jrs0.1J i;***, calculated by model; NA, not applicable.316 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343317Fig. 3. Representation offluid compartments in the SBM. (a) Schematic diagram ofa section ofthe arterial system, showing primaryand secondary arteries (adapted from Steffenson and Lomholt, 1992). This is the basis for the 2-compartment representation of theintravascular fluid volumes (IVFV1 and IVFV 2, or V1 and V 2) that is incorporated in the model. (b) Representation offluid compartmentvolumes in fish, including the IVFVs, the ISFV and the ICFV. The magnitude of the exchange of sodium between compartments i andj (indicated by arrows) is defined by the product of the permeability, Pijand the inter-compartmental differences in concentrations, CiyqC j. The gill permeability is PG and the concentration ofNa in the water is C w. (A complete summary ofthe notation and units isprovided in Table 1).fish, as configured in the model. The ambientwater, which is in direct contact with the outersurface of the branchial epithelium, is shown tothe left of the gill. The external water containsq q 2qNa , H and Ca . Beyond the role that each ofthese cations serves with regard to metal speciationand accumulation at the biotic ligand, as representedin the BLM (Di Toro et al., 1999, 2001;Paquin et al., 1999; McGeer et al., 2000; Santoreet al., 2001), they also exert more direct physiologicaleffects upon the ionoregulatory capabilitiesofthe organism itself. As discussed previously,qNa uptake is affected by the concentration ofqNa in the water via a Michaelis relationship,while the sodium efflux is affected to a lesserdegree by the ambient sodium concentration viaits effect on the concentration gradient that setsqpassive diffusion losses. Also, because Na isqexchanged for H , to maintain electro-neutrality,qpH is also expected to affect Na uptake as well.qFinally, since passive diffusion of Na occurs viathe paracellular junctions ofthe gill, and Ca 2qaffects the permeability of these junctions, Ca 2qhas a direct effect on ionoregulation as well. Giventheir effects upon ionoregulation then, it followsthat these constituents and the manner in whichthey affect ionoregulatory processes should generallybe considered in performing an ion balancefor an organism. Here, we will consider the effectsq 2qof Na and Ca , but will neglect the effect ofpH, given that the data to be analyzed reflectrelatively constant pH levels over time and acrosstreatment levels.The total body water ofa typical fish is equalto approximately 70% ofits wet weight, or approximately0.70 lykg w (700 mlykg w). As shown, thiswater is distributed among the three principal fluidcompartments ofinterest, the intravascular fluidvolume (IVFV, consisting ofa primary and secondarysystem), the interstitial fluid volume(ISFV) and the intracellular fluid volume (ICFV).IBM analyses ofpublished datasets, to be present-


318 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343ed subsequently, have provided estimates ofthesethree fluid volumes of 71, 99 and 530 mlykgwofthe total body water, respectively. As the bloodflows through the gill, it is separated from theexternal water by the branchial epithelium and,upon leaving the gill and circulating through therest ofthe body, it is separated from the interstitialfluid by the arterial wall. The interstitial fluid isin turn separated from the intracellular fluid bythe plasma membrane. The blood is filtered by thekidney (not shown) prior to returning to the gill.The primary and secondary systems flow in paralleland are connected by capillary-sized vesselscalled the arterial anastomoses (Vogel, 1985). Theflow of plasma passing through these vessels isreferred to as the plasma skimming flow rate, inpart because it removes very few red blood cellsfrom the primary system. This leads to a volumefraction of RBCs, or hematocrit, of only approximately1% in the secondary system, compared to25% or more in the primary system.With regard to sodium mass transfers, the modelis structured as follows. Transfer of sodium isallowed to occur across each ofthe interfacesmentioned above, the gill epithelium, the arterialwall and the plasma membrane. As discussedpreviously, the active uptake ofsodium from thewater that occurs at the gill takes place primarilyvia the chloride cells and conforms to Michaeliskinetics. Passive loss ofsodium from the primarysystem occurs via diffusion across the paracellularjunctions ofthe gill, from the higher plasmasodium concentration, C 1, to the lower ambientfreshwater sodium concentration, C w (the transferis in the reverse direction in salt water). The mostgeneral form of the model includes a transfer ofsodium between the primary and secondary arterialsystems at a rate corresponding to the plasmaskimming flow rate (Q ), between each ofthese12plasma volumes (V and V ) and the ISFV (V ),1 2 ISand between the ISFV and the ICFV (V IC). Thesodium concentrations in the ISFV and ICFV areCISand C IC, respectively. Finally, loss ofsodiummay also occur via renal excretion as blood in theprimary system is filtered by the kidney (notshown), prior to its return to the gill. The maindifferences between this representation and the 2-pool model presented by Nichols (1987) is thathere, losses occur from the primary compartmentofa 2-compartment plasma system, rather thanfrom the interstitial fluid, and also, the IBMincludes an intracellular fluid compartment.2.2.2. Model formulationThe model is described in terms of the differentialequations that govern the mass balance ofsodium about each of the four internal fluid compartments.The equation for each compartmentincludes terms for the relevant mass transfers ofsodium described above. The formulation proceedsas follows, beginning with the primary system:Rate ofchange ofmass ofNa in V 1sV dC ydtsJ yJ "J "J yJ (3)1 1 i e 12 1,IS rwhere Jiand Jeare the sodium influx and effluxrates, respectively, J12is the rate ofsodium masstransfer between the primary and secondary systems,J1,ISthe rate between the primary systemand ISFV, and Jrrepresents renal excretion. Notethat the units for volume (V in this equation) in1 ,this and in subsequent equations, are liters fluidper unit whole body wet weight, such that theunits ofeach term are mmol Naykg yd. Expresswing each ofthese mass transfers in terms ofthemore fundamental model parameters:C w1 1 M G 1 wCwqKMV dC ydtsJUyP Ž C yC .qQ12Ž C2yC1.qP Ž C yC . yPC (4)1,IS IS 1 r 1The first term on the right represents theMichaelis expression for the active uptake ofsodium from the external water, where J M* is themaximum or carrier-saturated uptake rate (mmolykg wet weight offishyday, or mmolykgwyd),corrected for inhibition due to exposure to themetal, KMis the halfsaturation concentration forqNa uptake from water and Cwis the concentrationqofNa in the external water. Consistent concen-tration units are used throughout. The inhibitedmaximum uptake rate, J M* is calculated from Eq.(2), as described previously, where the EC50 andb will be evaluated by calibration ofthe model toplasma sodium time series data using the BLMpredictedBL:Ag concentrations for each of theexperimental treatment conditions. Ifwarranted forother metals such as copper, KMcould be modifiedas well, though this would require a more complicatedmodel calibration procedure.The second term ofEq. (4) represents thediffusive exchange of sodium between the bloodand the ambient water. This exchange is proportionalto the product of a gill permeability coefficient,P (lykg yd) and the difference in theGw


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343321Wood, 1998; Grosell et al., 2000). Further, thehigher the rate ofloss ofsodium, the sooner itwill be for this critical level to be achieved, andthe shorter the survival time. The objective ofthemodel then is to predict the levels ofsodium inthe individual fluid compartments over time, keepingtrack ofprimary system plasma sodium levelsuntil such time as a 30% loss occurs, this timebeing the predicted survival time.To apply the model, it is necessary to firstevaluate the volumes ofthe fluid compartments ofinterest, the rates ofexchange between these compartments,and the size ofthe total exchangeablesodium pool that serves as a buffer for sodiumlosses from the considerably smaller plasma sodiumpool in the primary vascular system. The modelis calibrated by relating the degree ofinhibition ofsodium uptake to the predicted biotic ligand silverconcentration, such that the predicted decreases inplasma sodium levels are consistent with measuredresults. At that point it is suitable for use insimulating plasma sodium levels over time, andgiven the critical plasma sodium level associatedwith lethality, predicting survival time.3.1. Analysis of fluid compartment volumesThe first step then is to evaluate the fluidcompartment volumes. While much information isavailable in this regard, the results tend to varywith the method ofmeasurement. Holmes andDonaldson (1969) provide a comprehensive butsomewhat early review ofmethods ofmeasurementsand results, while Olson (1992) provides amore recent and updated review, one which focusesmore on the vascular system. The whole bodyfluid volume is readily determined from wholebody wet and dry weight measurements, and istypically in the range of70–75% ofthe wholebody wet weight (i.e. 0.70–0.75 lykg wet weight,or lykg w), for most fish. With regard to thevolumes ofthe individual compartments, the measurementmethod in most common use is the indicatordilution technique. This method involves useofany ofa number ofdifferent tracers, with eachhaving its own distinct advantages and disadvantages.Use ofthe indicator dilution technique toestimate volumes ofthe individual compartmentssimply involves the injection ofa known volumeand concentration ofa tracer into the blood,subsequent sampling to determine the resultingconcentration, and calculation ofthe relevant volumeofinterest by a simple dilution calculation.Because some tracers remain in the vascular system(e.g. radiolabeled red blood cells or Evansblue dye) while others are considered to diffusethroughout the extracellular fluid compartment(e.g. inulin), use ofan appropriate tracer providesa way to estimate the volume ofeither ofthesecompartments. The ICFV may be determined bythe difference between whole body water and theECFV.The disadvantage ofthe preceding approach isthat the concentrations ofthe tracer in the bloodwill change over time, as exchange with theinterstitial fluid occurs gradually, rather thaninstantaneously. Hence, the time ofsamplingbecomes an important consideration, with decreasingplasma concentrations measured with increasingtime, thereby leading to increasing estimatesofapparent dilution and fluid volume over time.This problem accounts for much of the variationin reported fluid compartment volumes (Steffensonand Lomholt, 1992). A kinetic modeling approachwill therefore be used to overcome this difficulty.That is, the SBM equations described previously,with active uptake set to zero, will be calibratedto time series data ofplasma tracer concentrations.The data to be analyzed are from two studies withrainbow trout. The first set of data was previouslyanalyzed by Nichols (1987), using a variety ofone, two and three fluid compartment representations,leading in one case to estimates ofthe bloodvolume of0.042 lykgwand ofthe extracellularfluid volume of approximately 0.17 lykg w. Thesecond set ofdata was reported and analyzed bySteffenson and Lomholt (1992), using equationsrepresenting a 2-compartment vascular system,with primary and secondary volumes of0.023 and0.048 lykg . wResults ofthe kinetic analyses ofthe two fluidcompartment tracer datasets that are consideredare summarized on Fig. 4. The originally reportedresults that were in terms ofconcentration havebeen normalized to the percentage ofthe initialdose to facilitate making a comparison on a consistentscale. The filled triangles represent theresults ofNichols (1987) and the open squares theresults of Steffenson and Lomholt (1992). Asshown, either set ofdata may be reasonably wellreproduced with an independent set ofparametervalues (upper and lower dashed lines). However,because there is no clear basis for accounting forthe differences between these two sets of results,


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343323whole body fluids, are known to be significantlyless than the plasma sodium levels (Olson, 1992),with the gradient maintained by a Donnan equilibriumcondition. An alternative approach is thereforefollowed to overcome this inconsistency. It isassumed that the sodium space, V , correspondsto the exchangeable sodium pool divided by theplasma sodium concentration: 50 mmolykgwy150mMyls0.33 lykg w. (The sodium space is the fluidvolume that would be associated with theexchangeable sodium pool of50 mmolykgwifthesodium contained in this volume was uniformlydistributed at a concentration equal to that oftheplasma sodium concentration.) The differencebetween this estimate ofthe sodium space and theECFV that was determined from the kinetic analysesdescribed above (VECsV1qV2qVISs0.17 lykg w) is assigned to an effective interacting ICFV(i.e. V sV yV s0.33y0.17s0.16 lykg ).IC Na EC wThe volume ofthe sodium space used here isconsistent with estimates ofthe radiosodium spaceof0.34 lykg made by Wood and Randall (1973).wWhile the interpretation ofthe ECFV used aboveis consistent with that ofNichols (1987), theinterpretation that the difference is associated withthe intracellular compartment is inconsistent withthe interpretation ofWood and Randall (1973).An alternative interpretation is that the exchangeablesodium pool (0.33 lykg w) represents thesodium associated with the extracellular fluid volumein its entirety. In this case, 0.17 lykgwwouldcorrespond to the more readily exchangeable, richlyperfused tissues (a fast pool) and the remainderof0.16 lykgwwould be associated with the extra-cellular fluid in the less accessible, less highlyperfused tissues (a slow pool). The equations andcomputational approach are independent ofthephysiological interpretation that is preferred.3.2. Analysis of plasma sodium dataWhile the preceding estimates ofthe fluid compartmentvolumes are not considered to be definitive,the important consideration is whether or notthis representation can serve as a reasonable basisfor predicting the kinetics of plasma sodium lossesover time. As a first test of this capability, themodel will be applied to a dataset where therainbow trout were exposed to 3.2 mgyl ofsilver,while chloride was varied, and plasma sodiumlevels ofthe fish were monitored over the ensuing48 h (McGeer and Wood, 1998). The variation ofNachloride levels is important, as chloride formssilver chloro-complexes, primarily AgCl, and thisform of silver has been shown to markedly reducethe bioavailability ofsilver to rainbow trout (Buryet al., 1999a,b). In the context ofthe silver BLM,at a fixed dissolved silver concentration, when thechloride concentration is low, silver availability ishigh, and the predicted BL:Ag will be high. Then,as the chloride level increases, silver availabilitydecreases, resulting in a decrease in BL:Ag. Recallit is a premise ofthe SBM that the response bythe organism to exposure to silver, in this case theinhibition ofthe active uptake ofsodium from thewater, will be directly related to the concentrationofBL:Ag. Hence the degree ofresponse by thefish should reflect this change in BL:Ag. What isrequired then is to establish this relationship thatis expressed in the form of Eq. (2). This analysisis summarized next.The equations presented previously that describethe sodium balance of a freshwater fish will besolved numerically to simulate the plasma sodiumresults. To do so, it is necessary to assign valuesto a number ofmodel inputs. The values oftheseinputs are listed in Table 1 under the heading‘Plasma sodium simulations’. First, the Michaelisparameters that define active sodium uptake kineticsare required. Initial assignments were J s0.5 Mmmolykgwyhs12 mmolykgwyd and KMs0.04mM for sodium. The value for J is a typicalvalue for rainbow trout, and is consistent with theuninhibited sodium uptake curve shown previouslyon Fig. 2. The halfsaturation constant is notreadily defined, a priori, but it is known that itwill vary with acclimation conditions. McDonaldand Rogano (1986) present results which indicate,qualitatively at least, that the KMfor sodium andchloride will vary in rough accordance with theNa and Cl concentration ofthe acclimation water,such that the basal ion-transport rate is maintained(i.e. for JM constant, if KMsC w, then Jiis always50% of J M). Bury et al. (1999a) also provide datato indicate this is a reasonable first approximation.The sodium KMwas therefore set equal to thesodium concentration ofthe acclimation water,0.04 mM, which is the same concentration as wasused in the toxicity tests to be analyzed. Next,recalling that the overall balance ofsodiumincludes renal losses, the parameter controlling thisprocess was set to achieve a loss 10% oftheuninhibited sodium influx rate, a representativevalue (Wood, 1989; Curtis and Wood, 1991;M


324 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343Fig. 5. Plasma sodium time series data (" standard error) are shown for rainbow trout control fish (Ags0) and fish exposed to 3.2yymgyl ofdissolved Ag, as Cl varies (data: McGeer and Wood, 1998). Results are shown for (a) control fish, Cl s0.014 mM, BL:Agsy0 and Ags0, followed in order of decreasing chloride and increasing predicted biotic ligand silver: (b) Cl s1.44 mM, BL:Ags3.4y y ynmolyg w; (c) Cl s0.538 mM, BL:Ags6.4 nmolyg w; (d) Cl s0.292 mM, BL:Ags8.3 nmolyg w; (e) Cl s0.115 mM, BL:Agsy10.3 nmolyg w; and (f) Cl s0.014 mM, BL:Ags12 nmolyg w. The upper horizontal solid reference line represents the presumed constantsodium concentration in the absence ofexposure to silver. The other four lines, in order oflowest to highest lines, show the predictedsodium concentrations in the IVFV 1 (the lowest solid line, to be compared to the plasma sodium data), IVFV 2, the ISFV and the ICFV.Wood, 1992). Finally, it is necessary to define thegill permeability, which is estimated by assumingsteady state applies under pre-toxicity test conditions,and evaluating PGofrom Eq. (7) and PGfrom Eq. (5), as described previously. (If J andC1have not been measured, they would need tobe assigned on the basis ofrepresentative values.)For the plasma sodium and survival time analysesto be presented herein, it is assumed that J s0.5 Mmmolykgwyhs12 mmolykgwyd; KMsCws0.04or 0.05 mmolyl (such that f s0.5); J s10% ofJis fNaJ M (10% ofpre-toxicity test sodium influxrate). Based on these assumptions, it follows thatPGos0.0378 lykgwyd.It remains to specify a relationship between thedegree ofinhibition ofthe active uptake rate ofsodium, J M, and the BL:Ag concentration, as thisNarMsets the magnitude ofthe term representing theactive uptake rate ofsodium in Eq. (4). TheBL:Ag is first evaluated with the previously developedsilver BLM (Paquin et al., 1999) with thetoxicity test water chemistry specified as inputsfor each of the treatments. The parameters of thedose–response curve, the EC50 for uptake inhibition,and b, which characterizes the slope oftheresponse, are adjusted by calibration to theobserved response in plasma sodium data. Theresults ofthe SBM simulation analysis are comparedto the rainbow trout plasma sodium data onFig. 5 and the dose–response curve that is used toachieve this fit of the plasma data is shown onFig. 6. The plasma sodium time series data("standard error) are shown for the controls(Ags0) on Fig. 5a. Some unexplained variability


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343325Fig. 6. Does response curve for percent inhibition of JMas a function of BLM-predicted BL:Ag. Dose–response curve parameters ofEC50s15.8 nmolygwand bs0.278 are based on calibration ofthe 4-compartment SBM to the plasma sodium data ofFig. 5. Pointsindicated along the curve correspond to the estimates ofBLM-predicted BL:Ag for conditions ofthe three silver datasets analyzed withthe SBM: m, McGeer and Wood, 1998 (Fig. 5); e, Galvez and Wood, 1997, chloride treatments (Fig. 8), and q, Galvez and Wood,1997, calcium treatments (Fig. 9; shown here as overlapping points at BL-Ag;30 nmolygwand ;95% inhibition; they also coincidewith some ofthe low chloride treatment results, e).is evident, as control fish plasma sodium levelswould be expected to remain approximately constantover the 48-h test duration. These changesare likely to be within the range ofnormal physiologicalvariation, and may also reflect samplingand analytical variability. With regard to the modelresults, the solid line, the initial condition is setequal to the average concentration over the testduration, and it remains constant in time. This isbecause the gill permeability was evaluated suchthat the uptake and loss terms were in equilibrium,and because the BL:Ags0, there is no inhibitionof sodium uptake for the control fish.Fig. 5b through Fig. 5fpresent comparisons ofmodel results to the plasma sodium data for theremaining 3.2 mgyl dissolved Ag treatments,shown in order ofdecreasing levels ofchloride,from 1440 to 14 mM and increasing levels ofpredicted BL:Ag (3.4–12 nmolyg ; see captionwfor values for each treatment). At the highestchloride level (1440 mM; Fig. 5b), the predictedBL:Ags3.4 nmolyg , resulting in less than 1%wuptake inhibition for the response curve of Fig. 6.Thus, the decrease in plasma sodium concentrationrelative to the initial condition (set to the averageofthe initial and 1-h measurements) is negligibleover the 48-h test duration, well within the limitsofthe measured plasma sodium levels. As chloridelevels are progressively decreased in the remainingtreatments (Fig. 5c–f), a clear pattern ofincreasinglysevere plasma sodium losses (i.e. decreasingplasma sodium concentration) is evident in thedata. Because the predicted BL:Ag also increaseswith decreasing chloride levels, resulting in anincreasing degree ofinhibition ofsodium uptake,the model results follow the same trend as thedata, with progressively higher losses ofsodiumover time as chloride levels decrease. Note thatthere are five lines, corresponding to predictedconcentrations in each ofthe four compartmentsplus an initial condition reference line, are displayedon each panel, although the different linesare only discernible on Fig. 5c–f. In each case,the lowest solid line curve represents the predictedprimary system plasma sodium result, and is thecurve that should be compared to the data. Thenext higher three curves, in order ofthe lowest tothe highest, show the predicted sodium results forthe secondary vascular system, the ISFV, and theICFV, respectively. (The upper horizontal line is


326 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343shown as a point ofreference, indicating the initialplasma sodium level that would persist in theabsence ofany inhibition ofactive uptake.)The fit of the plasma sodium data of Fig. 5 wasachieved by assigning the IPCs a value of0.1lykg yd in all cases. As a general rule, the lowerwline, representing the computed primary systemplasma sodium level, reproduces the measuredtrends in plasma sodium quite well. Sodium levelsin the remaining compartments tend to track theconcentrations in the primary system rather closelywhen the rate ofdecrease occurs slowly (Fig. 5cand d), but lag progressively further behind as therate ofloss increases (Fig. 5e and f). The reasonfor this to occur, as accounted for in the contextofthe SBM described here, is that the fluxesbetween compartments limit the rate ofexchangeofsodium between compartments. Thus, whenplasma sodium losses occur quickly, equilibrationwith the other compartments must necessarily lagbehind. The degree ofthis lag is related to thevalue of the permeability coefficients that havebeen evaluated. The values ofthe permeabilitycoefficients are necessarily approximate due tolimitations ofthe types ofdata that were used toperform the evaluation.The results ofFig. 5 demonstrate the ability ofthe IBM for sodium to predict plasma sodiumlevels over time. This is an important capability,because it is a simple matter for computationssuch as those presented on Fig. 5 to be extendedin time until the critical plasma sodium concentrationassociated with lethality is reached, with thattime being the predicted survival time. Further, animportant benefit ofthis initial analysis ofplasmasodium levels is that it provides an estimate oftherelationship between the BLM-calculated BL:Agand the percent inhibition ofactive sodium uptake.The resulting dose–response relationship is shownon Fig. 6. The EC50 for inhibition of JMis 15.8nmolyg and the slope ofthe dose–response curve,wb, is 0.278. The filled triangles indicated on thiscurve correspond to the calculated BL:Ag levelsassociated with the 5 silver treatments shown onFig. 5. Note that for the range of BL:Ag levelsconsidered, 3.4–12 nmolyg w, the percent inhibitionof J ranges from approximately 1% to somewhatMless than 30%. As will be discussed subsequently,these results have significant implications withregard to the longer-term effects to be expected.3.3. Analysis of survival time dataThe preceding analysis ofplasma sodium levelsserved as a basis for estimating the parameters ofdose–response curve ofFig. 6. The other two setsofplot symbols indicated on the curve ofFig. 6correspond to the percent inhibition that is associatedwith the BL:Ag levels that are predicted forthe treatment conditions ofthe two survival timedatasets that are to be analyzed next (Galvez andWood, 1997). In these experiments, rainbow troutwere exposed to approximately 100 mgyl ofsilver2q(nominal) and either Ca , added as eitheryCaSO4 or Ca(NO 3) 2, or Cl , added as KCl ofNaCl, were varied from 50 to 5000 mM. The 50%survival time, the ET50, was the end-point in theseexperiments. While the concentration ofsilver thatwas used in these tests was considerably in excessofan environmentally relevant exposure level(Campbell et al., 2001), the results are quite usefulbecause the additions ofeither calcium or chlorideresulted in a wide range ofmedian survival times,from less than 1 h to )7 days, the duration ofthetest. The cluster of q signs at BL:Ag)30 areassociated with the calcium dataset, and indicatethat active sodium uptake is predicted to be almostcompletely suppressed for all of the treatments inthis set ofdata, with little variation across treatmentlevels. Conversely for the chloride dataset,the BL:Ag and hence the predicted inhibition ofthe active uptake ofsodium varies over a muchwider range (open diamond plot symbols), fromapproximately 5% inhibition to 95% inhibition.This range ofresults highlights the importance ofAg complexation by chloride as a means ofmitigatingthe availability and toxicity ofsilver torainbow trout.As a preface to a discussion of the next set ofresults it is useful to first consider what should beexpected when nearly 100% inhibition ofactiveuptake ofsodium occurs, as is predicted for thecalcium experiments. It is readily shown fromsimple mass balance calculations that a 30% lossofthe exchangeable sodium pool of50 mmolykg w (i.e. a loss of15 mmolykg w) would requireapproximately 2.5 days at a net efflux of 6 mmolykgwyds0.25 mmolykgwyh (at JMs12 mmolykgwyd and f Nas0.5). All other things equal, thiswould be the shortest survival time to be expected.However, it turns out that this time estimate isactually much longer than the range ofsurvivaltimes that were observed in the calcium treatment


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343327experiments to be reviewed next (-1 h to approximately9 h) and in the lower chloride treatmentsas well (-1 day at up to 500 mM ofeither NaClor KCl). Ifit is assumed that the permeability ofthe exchange surfaces with the primary system aretoo low for the other compartments to deliversodium at a fast enough rate to offset the lossfrom the primary system, which contains only 7%ofthe exchangeable sodium pool, then the survivaltime could be reduced to as little as approximately4h(i.e. a loss of30% of3.5 mmolykg , or aboutw1 mmolykg is required). This is in much closerwagreement with the shortest reported survival timeofapproximately 0.75 h, but still about a factor of5 too long. It appears that the reason for thediscrepancy is that the foregoing calculations donot consider the likelihood ofan increase in gillpermeability, a result ofphysical damage to thegill during short-term pulse exposures to highconcentrations of metals, much like the effects thathave been observed for low pH conditions whereorder ofmagnitude or greater increases in permeabilitywere estimated to have occurred (Packerand Dunson, 1970, 1972; McDonald et al., 1983).A plausible mechanism for the increase in gillpermeability is that damage to the gill occurs as aresult ofdisplacement ofcalcium from the calcareousmaterial that comprises the paracellular junctionsbetween cells ofthe gill epithelium. It is thisintercellular cement that maintains the physicalintegrity of the gill. This effect has been seenpreviously to occur under acidic conditions, wherethe calcium is titrated from the gill by protons(Milligan and Wood, 1982; McDonald, 1983a,b)and could reasonably be expected as a mechanismfor the deterioration of the gill epithelium bymetals as well. The increase in permeability iscaused by a decrease in the depth ofthe paracellularjunctions as the calcareous intercellularcement is titrated away (McDonald et al., 1991).Here, it is assumed that the calcareous materialdeteriorates as a result ofdisplacement ofcalciumby free silver, while increasing the level of Ca 2qtends to reverse the direction ofthis displacementtypeofreaction. Alternatively, adding chloridereduces the free silver, resulting in a similar beneficialeffect, but for a different reason. Note thatthis reaction should not be interpreted as an equilibriumreaction, as this is probably not the case,at least under conditions ofa pulse exposure.Rather, there would be expected to be a progressivedeterioration ofthe gill, until such time as theorganism is able to adapt during conditions thatare less extreme, or until mortality occurs. It isthis line ofreasoning that leads to the form oftherelationship described above (Eq. (9)) which willbe applied to adjust for changes in permeabilityqwhen Ag is greater than approximately 35 mgyl.Note that the effect of chloride on gill permeabilityis indirectly accounted for in this relationship viaits effect on the free silver concentration.Fig. 7 shows how this approach is applied withthe survival time data for the calcium treatments.The open and filled triangles represent results forcalcium additions in the form of Ca(NO 3)2andCaSO 4, respectively. The model is used in thesame way as in the analysis ofthe plasma sodiumdata, using the same dose–response curve (Fig.6), in conjunction with the BL:Ag estimated withthe BLM, to predict the degree ofinhibition ofJMfor each set of test conditions. Plasma sodiumconcentrations are then computed over time, untila 30% decrease occurs. The time at which thisoccurs is the estimated ET50 for survival time.Because the model does not incorporate any mechanismfor distinguishing between the effects of thetwo added anions, either chemically or physiologically,only one line is shown for the model results.The model results are consistent with the survivaltime data, which also fail to display any systematicvariation with regard to the form in which the Cawas added. Both measured and predicted survivaltimes increase from approximately 1htoslightlymore than 8 h over the range ofcalcium treatmentlevels tested. Consistent with the preceding analysisof gill permeability coefficients, the gill permeabilityhas been increased by a factor ofapproximately 5.6 at the lowest calcium levels,and by about a factor of slightly more than 2 atthe highest Ca levels. This is achieved via Eq. (9)y4qwith as3.09=10 for Ag in units of mgyl(4.54 if mM units), bs2.05 and csy0.222q(Ca in mM units).Finally, consider the effect of increasing thechloride concentration on survival. The results aresummarized on Fig. 8, where the scale ofthe y-axis is increased by 20-fold relative to Fig. 7 (theresults for the calcium treatments). As shown,addition ofup to 5 mM chloride (as either KCl orNaCl), the same increase in molar concentrationas for calcium, increases the survival time ET50from less than 1 h to approximately 7 days orlonger. For KCl additions (m), the model (solidline) predicts a median survival time ofapproxi-


328 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343Fig. 7. Comparison ofpredicted (solid line) with measured ET50 for rainbow trout exposed to ;100 ugyl silver and variable treatmentsofCaSO 4 (m) or Ca(NO 3) 2 (D). Results obtained with sodium JMs12 mmolykgwyd and KMs0.05 mM, PGos0.0386 lykgwyd, PP,ISsPIS,ICs0.1 lykgwyd. (Data: Galvez and Wood, 1997).Fig. 8. Comparison ofpredicted with measured median survival times for rainbow trout exposed to ;100 ugyl silver and variablelevels ofKCl (datasm and modelssolid line) and NaCl (datasD and modelsdashed line). The data point for the high NaCl treatment(5 mM) is plotted at the 7-day test duration (≠), but actually exceeded 7 dayss168 h (i.e.-50% mortality was observed thru the 7day test duration) while the model predicts the fish will survive. (The model predicts survival at KCl);2 mM and at NaCl);1mM). Model parameter values are same as for calcium treatments of Fig. 8. (Data: Galvez and Wood, 1997).


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343329mately 1hatthelowest chloride level, 0.5–3 daysat the intermediate chloride levels, and for anindefinite period of time at the highest chloridelevel, with all but the result at the highest chloridetreatment in good agreement with the data. Thediscrepancy at the highest treatment level could beeliminated ifthe gill permeability ofthe controlfish was increased by somewhat less than a factorof 2, a difference expected to be within the limitsofexperimental variability and the uncertainty ofthe equilibrium assumptions used to evaluate controlfish gill permeability.With regard to the NaCl treatments (n), thepredicted BL:Ag levels are similar to the predictedlevels when KCl is added. However, in conformitywith the data, the model predicts an increase insurvival time in comparison to the KCl treatmentswhen the chloride is added as NaCl. The reason isqthat there is an increase in Jiwhen Na is addedin association with the chloride, due to the factthat the uptake rate ofsodium is related to thesodium concentration in the external water via theMichaelis formulation (Eq. (1)). For the highestNaCl addition, the ET50 value was reported to begreater than approximately 7 days, the value indicatedon the graph, because less than 50% mortalitywas observed over the 7-day duration oftheexperiment. The model result is consistent withthis observation, predicting rainbow trout survivalfor this set of treatment conditions.As with all ofthe calcium results, chloridetreatments ofless than 1 mM led to survival timesof -2 days, less than could occur even with 100%inhibition ofsodium uptake. The preceding analysisof gill permeability coefficients indicated thatthe permeability apparently increased at free silverlevels in excess ofapproximately 37.5 mgyl. Assuch, the explanation ofsurvival times ofless than2 days is attributed to this factor. As discussedqpreviously, the effect of Ag on gill permeabilitywas represented via Eq. (9), with PGreturned toqbaseline conditions when Ag is less than 37.5mgyl. By adopting this approach the model wasable to predict survival times over the range oftest conditions in the chloride experiments.4. DiscussionNumerous models have been proposed over thelast 20 years for use in predicting the survivaltimes ofaquatic organisms exposed to either metalsor organic chemicals. These models may beroughly classified as chemistry-based models (Royand Campbell, 1995), bioaccumulation-basedmodels (Mancini, 1983; Connolly, 1985; McCarty,1987; McCarty et al., 1993; Meyer et al., 1995;Marr et al., 1998), physiologically-based models(Szumski and Barton, 1983), and combinationsand variations thereof (Breck, 1988; Verhaar etal., 1999). Here, a generalized physiologicallybasedmodeling framework is presented that maybe used to evaluate the survival time ofaquaticorganisms exposed to metals. It is applied in theanalysis ofdata for rainbow trout exposed to silver.The model framework is similar in some ways toa PBPK model, but not entirely. While the modelis founded upon a physiologically-based, 4-compartmentrepresentation ofa fish, and it includesaccumulation ofthe metal at the site ofaction oftoxicity, it differs from a conventional PBPK modelin that it does not compute the internal distributionand ultimate disposition ofthe stressor, inthis case silver, over time. Rather, the concentrationofsilver at the site ofaction, as calculatedusing the previously developed BLM, is used toevaluate the degree of effect of silver on themechanisms oftoxicity, inhibition ofthe activeuptake of sodium and, at sufficiently high levels,on the passive diffusive losses. It then accountsfor the subsequent impact of these changes inuptake and loss ofsodium by keeping track ofthecumulative damage to the fish, as manifested byloss of sodium from the internal fluid compartments.Survival time corresponds to the time whenthe cumulative effect is a fixed degree of loss ofsodium, taken here to be 30%, from the primaryvascular system. It is expected that the capabilityto perform this type of evaluation, to assess cumulativedamage to the organism over time, will offerregulatory agencies an improved basis for explicitlyconsidering magnitude, duration and frequencyofoccurrence when developing updated WQC formetals. Subject to further refinement, it may alsobe useful in extrapolating from acute to chroniceffect levels, and in other areas as well, asdescribed below.4.1. Analysis of indicator dilution and plasmasodium dataThe analyses ofthe tracer data and the plasmasodium data were performed, in part, to evaluatethe sizes of the four fluid compartment volumesand the rates ofexchanges between them. It was


330 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343possible to achieve a reasonable fit of both typesofdata using fluid compartment volumes that aregenerally consistent with compartmental volumesthat have been reported in the literature (Figs. 4and 5). The inter-compartmental permeability coefficients,or IPCs, were evaluated concurrently withthe fluid volumes for the indicator dilution tracerdata and were preliminarily set at 0.08 lykg yd. wThe same fluid volumes were used in the analysisofthe plasma sodium dataset (Fig. 5) and an effortwas made to fit this dataset by adjusting the IPCsindependent ofthe values that had been used forthe tracer studies. The model is fairly sensitive tothese coefficients because an increase or decreasein the IPCs results in a corresponding increase ordecrease in the rate ofplasma sodium loss as well.The reason is that use ofrelatively high IPCsresults in an effective increase in the plasmasodium pool that is available to buffer losses ofsodium from the primary system, while a decreasehas the converse effect. As it turns out, the datawere not of sufficient detail to justify the independentevaluation of each of the different IPCs(P , P and P ) and a value of0.1 lykg1,IS 2,IS IS,IC wyd was assigned in all cases.There was not any a priori reason to expect thatthe IPCs that were evaluated for the indicatordilution studies performed with inulin and theplasma sodium studies would have the same values.Rather, it would have been reasonable toexpect that the permeability coefficients for sodiumwould be considerably higher than for thetracers that were used in the indicator dilutionstudies (McDonald, personal communication).However, it was decided that the slight differencebetween the values of the coefficients that wereinitially assigned based on calibration to the measuredconcentration data (0.08 vs. 0.10 lykg yd) wcould not be justified on the basis of the fit of thedata by the model that was achieved. It wastherefore decided to assign a consistent value ofPijs0.1 lykgwyd for both sets of data. It isemphasized that although the model was able tofit both types of data with a single set of permeabilitycoefficients, this should not be interpreted tobe an indication that the values of these coefficientsdid not in fact differ significantly. Rather, itis more likely an indication ofthe limited discriminatorypower ofthe model with regard to theinterpretation ofthese data, as well as the practicallimitations associated with what are otherwisejudged to be excellent and relatively detaileddatasets.Together, the fluid compartment volumes andpermeability coefficients are important model parameters,as they control the response time oftheplasma sodium pool when active uptake is reducedandyor permeability increases as a result ofphysicaldamage to the gill. However, the analysis ofthe 24-h tracer dataset was judged to be oflimiteduse in evaluating what is, ostensibly, the ICFV, aswell as the rate ofinteraction between this compartmentand the remainder ofthe fluid volume,the ECFV. The plasma sodium results indicate thatat PIS,ICs0.1 lykgwyd, the rate ofexchangebetween the extracellular and intracellular fluidcompartments was not rapid, as the calculateddecrease in concentration in this compartment,even in the most extreme test case, was alwaysless than 5% over the 48-h test duration (Fig. 5f).While it is not entirely clear that the modelshould include interaction with the ICFV, there issome precedent for structuring the model in thisway. Investigations of the effect of low environmentalpH on rainbow trout provide evidence ofthere being a significant contribution by the ICFVto total body ion losses, including sodium losses(McDonald and Wood, 1981). These losses ofions, which initially occur from the blood, lead tothe establishment ofosmotic and ionic gradientsthat induce shifts of both fluid and ions betweenthe ECFV and ICFV (McDonald and Wood, 1981;Milligan and Wood, 1982). Because it is wellknown that both acidic conditions and exposure tometals, such as silver and copper, result in loss ofions from the blood, it is reasonable to expect thatthe ICFV would respond in a similar manner ineither case, regardless ofthe underlying cause ofthe ion depletion (i.e. exposure to low pH conditionsor to metals). An alternative interpretation ofthe fluid compartments considered herein is thatthey correspond to a 2-compartment vascular systemexchanging with a 2-compartment ISFV, whilethe ICFV is a non-interacting volume. The ISFVin this case would correspond to a 2-compartmentsodium pool consisting ofrichly perfused tissuesthat are readily accessible for exchange, a ‘fastpool’, and tissues that are less well perfused, a‘slow pool’. As configured herein, the slow poolis connected to the vascular system via the fastpool (i.e. the 2 pools are connected in series).There are a number ofalternative configurationsofthe fluid compartments that could reasonably


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343331be considered. The simplest would be to considera single, completely mixed, fluid volume. Thisapproach was used in the early stages ofmodeldevelopment and it was found to be necessary toincrease the effective volume of the fluid compartment,as survival time increased, to achieveconsistency in response times between model anddata. (The version ofthe model described hereinmay be set up in this way by the appropriateassignment ofinputs.) Another approach would beto allow both ofthe extravascular fluid volumesto exchange directly with the vascular system, withthe exchange rates between the blood and the fastand slow pools controlled by varying the respectivepermeability coefficients. Another variation wouldbe to have the tissues associated with the fast poolexchange with the primary vascular system andthose ofthe slow pool exchange with the secondaryvascular system. The model would need to bemodified slightly to represent these latter configurations.It is not clear ifthese distinctions wouldlead to a material change in the ability ofthemodel to reproduce the observed results, but theycould potentially lead to an improved physiologicalrepresentation ofthe fish. It is expected that thecontinued use ofthis model, including modelsensitivity analyses in conjunction with analysis ofresults ofsuitably designed experiments, will leadto an improved understanding ofhow best toproceed.Recently, another excellent source ofinformationon tissue fluid volumes in fish has beenidentified (Bushnell et al., 1998). This study providesvery detailed information on fluid volumesfor a wide variety of tissues. Of particular interestwas their evaluation ofthe volume ofthe secondaryvascular system, and its rate ofexchange withother compartments, both ofwhich were found tobe ofmuch less importance than the results reportedby Steffenson and Lomholt (1992). Furtherconsideration ofthese results will be warranted inconjunction with future applications of the IBM.4.2. Analysis of survival time dataThe survival time data analyzed herein serve asan excellent basis for model development becausethe water chemistry ofthe test waters reflected awide range ofconditions that resulted in a correspondinglywide range of effects. Median survivaltimes ranged from less than 1 h to longer than 1week. While having its advantages, to some degreethe wide range oforganism responses was alsoproblematic, as it resulted in the need to introduceadditional model parameters to represent each ofthe mechanisms oftoxicity that are reflected in thedata. The discussion that follows will be orderedin accordance with the different time scales consideredby the model, beginning with the shortertermpulse exposure results followed by theintermediate range effects. The potential for applicabilityof a refined version of this model frameworkto the analysis of chronic effect conditions,conditions not fully reflected in the data that havebeen analyzed herein, will also be discussed.4.2.1. Short-term pulse exposuresTwo sets ofexperimental results were analyzedin which lethality occurred on time scales ofaboutan hour to a few days. To achieve the rapid onsetoflethality, it was necessary to invoke an assumptionthat there is physical damage to the gill,leading to an increase in gill permeability and anaccelerated rate of losses due to passive diffusionfrom the blood. Based on studies at low pH, it hasqbeen found that the Na efflux increases progres-sively as pH decreases (McDonald, 1983a,b). Itcan be increased markedly, by more than 10-fold,at pH 4 (Packer and Dunson, 1970). With influxessentially eliminated at this pH, the sodium effluxqresulted in a rate ofloss ofNa from the body ofapproximately 10% per hour. At pH 3, the rate ofqNa efflux increased to 50% per hour and rapidlyresulted in death (Packer and Dunson, 1972). Themechanism of this increase in efflux has beenattributed to an increase in permeability caused bylow pH titration ofthe calcium-based intercellularcement-like material that the tight junctions ofthebranchial epithelium are made of. This effectappears to be similar to what happened in the lowcalcium and low chloride datasets analyzed previously,where it was necessary to increase gillpermeability by as much as about a factor of 6 toaccount for the short survival time that wasobserved.Packer and Dunson (1970, 1972) provided someofthe earliest demonstrations that exposure ofbrook trout to low pH conditions inhibits sodiumuptake and that it is the rate ofloss ofsodium,rather than the total amount that is lost, thatcorrelates best with survival time. Similar effectshave been reported by others (McDonald, 1983b;Wood, 1989). Packer and Dunson (1972) hypothesizedthat ‘extremely rapid rates ofloss may


332 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343deplete plasma Na to a greater extent than iftherate is slower and the loss comes from a greaterproportion ofthe total Na pool.’ This was concludedfrom the observation that when the rate ofbranchial sodium loss and mortality was acceleratedthe whole body Na loss was reduced. (Overalllosses ofsodium by brook trout were well inexcess of30% in these early studies.) A similarstatement may be made about the SBM. That is,ifthe loss ofsodium occurs relatively slowly, thensodium levels in all ofthe compartments willdecrease at nearly the same rate, and the wholebody sodium loss will approach 30% at the timeofdeath. Conversely, ifsodium is lost quicklyfrom the primary system, then the decrease ofsodium in the other compartments will lag behindthe concentrations in the primary system and lesssodium will be lost, on a whole body basis, at thetime ofdeath.The criterion that has been used here ofa 30%loss ofplasma sodium at the time ofdeath isemployed as a first approximation, and could berefined if justified on the basis of a more thoroughreview ofthe available data. It should also berecognized that use ofa 30% decrease in theplasma sodium level is somewhat ofan oversimplification,as it is the overall disruption of ionoregulationthat actually leads to adverse effects tothe organism. These effects include changes in theosmolality of the blood, shifts in fluid volumesand an ensuing and well-documented cascade ofevents that culminates in cardiovascular collapseand death (Milligan and Wood, 1982; McDonald,1983b; Wood, 1989 for effects of pH; also Wilsonand Taylor, 1993a; Taylor et al., 1996 for copper,Wood et al., 1996; Hogstrand and Wood, 1998 forsilver). Sodium has been used herein as a convenientbiomarker, a surrogate for the overall effecton ionoregulation that triggers this ill-fatedsequence ofevents.The effect of calcium on gill permeability, acompetitive interaction with silver at the gill paracellularjunctions, is not to be confused with thecompetitive interaction that is represented in theBLM ofacute toxicity. The competitive interactionin the BLM represents competition at the bioticligand and is related to the inhibition ofNKAactivity, rather than an effect on permeability. Atmore realistic levels ofdissolved silver ofapproximately6–8 mgyl, Janes and Playle (1995) haveshown that calcium is ineffective at competingwith silver for interaction at the biotic ligand atcalcium levels as high as 10 mM. Here, eventhough the dissolved silver concentration is muchhigher, there is evidently a significant benefitassociated with increasing the calcium from 0.05to 5 mM, as survival time increases by about anorder ofmagnitude.The model results described herein have emphasizedthe role ofCa in the model, both with2qrespect to its role as a competing cation (in theBLM), as well as its effect on gill permeability(in the IBM). However, Schwartz and Playle(2001) have recently reported results that support2qthe inclusion ofMg in the BLM for silver as acompeting cation as well, with its role generallyviewed as being lesser in importance than that of2qCa . The reason for this lesser role may be2qrelated to the fact that Ca has the added effecton gill permeability through its ability to stabilizethe gill structure, which is comprised ofa calcareousmaterial. In any case, the competitive effectofeven calcium tends to be ofless importancethan it appears to be for other metals (Hogstrandet al., 1996). This reduced benefit is accountedfor, in the context of the Ag BLM, by the relativelyhigh affinity of Ag in comparison to that of othermetals for binding to the biotic ligand.4.2.2. Intermediate-term exposuresAs indicated by the short survival times reportedby Galvez and Wood (1997), these data appear tohave reflected conditions where gill permeabilitywas elevated due to the high silver concentration.The exception to this appears to have been in theintermediate to high chloride level experimentswhere survival times exceeded approximately 2days. Speciation calculations indicate that the freesilver was less than approximately 35–40 mgyl inthe experiments where survival times were greaterthan approximately 2 days and greater than thiswhen the survival time was substantially less than2 days. Since ambient levels ofsilver are typicallymuch less than this (Campbell et al., 2001), itisunlikely that physical damage to the gills offishwill occur under normal field conditions. Themodel provided a reasonable prediction ofsurvivaltimes at a chloride level of1 mM, but overpredictedsurvival at 5 mM. The reason for this inthe high KCl treatment may have been that thegill permeability ofthe control fish was apparentlyless than the exposed fish. In the high NaCltreatment, both model and data indicated the EC50


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343333would not occur within the time limits oftheexperiment.4.2.3. Acclimation and chronic toxicityOne ofthe motivating factors that led to thedevelopment ofthe SBM was the idea that it mighthelp to better understand, and ultimately to bebetter able to predict, the effects that result fromlonger-term chronic exposure to metals. It hadbeen shown that the rate ofresponse ofplasmasodium levels to exposure to silver decreased asthe concentration ofavailable silver decreased(Fig. 5; McGeer and Wood, 1998). At about thesame time, there were also data that showed thatat silver levels of0.5–2 mgyl rainbow trout mayeventually recover from an initial loss of sodium,with the recovery taking place over a time scaleofapproximately 28 days (Galvez et al., 1998).There is a suggestion ofthis same response in thedata ofFig. 5c and d where, between the time ofthe 24- and 48-h measurements, qualitatively atleast ifnot statistically significantly, there appearsto be either a leveling off or slight increase in theplasma sodium level. Although the appearance ofacclimation was a positive finding, other resultsfrom even longer-term studies have shown thatreduced survival may still be observed over alonger period ofapproximately 18 months, at stilllower silver concentrations of0.2 mgyl (Davies etal., 1978). One explanation for why the rainbowtrout in these longer-term experiments apparentlydid not fully acclimate is that it may be necessaryfor the metal exposure level to first exceed athreshold level that causes a detectable morphologicaldisturbance (McDonald and Wood, 1993). Itis plausible that the very low exposure levels usedin these well-controlled tests precluded this condition.It follows that under conditions of a morenatural setting, short-term periods where concentrationsare elevated above the average concentrationmight be beneficial in that they may stimulatethe physiological changes that lead to acclimationover the long term.Returning to the model, the initial line ofreasoningwas that at very low silver concentrations,the organism response to a loss ofplasma sodiumwould still occur, but at a very slow rate. Givensufficient time, the critical plasma sodium levelwould eventually be reached and mortality wouldoccur. What was needed then was for the modelto be able to relate the exposure level to the degreeofinhibition ofactive sodium uptake, and henceto the net rate ofloss ofsodium, and to then usethis relationship to predict the response ofplasmasodium levels to chronic low-level exposures. Themodel was developed and, within reasonable limits,it has been shown to be able to achieve theseobjectives with a reasonable level ofsuccess.Interestingly, however, it does not respond in themanner that had been originally envisioned by thedevelopers ofthis model. Rather, it does what afish does. That is, ifthe degree ofinhibition islow, in the range of5–10%, then plasma sodiumbegins to decrease slowly, but eventually it willstabilize at a new steady state condition. This isexactly the situation that is illustrated by both themodel and data shown on Fig. 5c and d. Thesimple explanation for this is as follows. Undernormal conditions, influx and efflux are in balanceand the plasma sodium level is constant. Iftheywere not in balance, there would be a net rate ofgain or loss ofsodium, and plasma sodium levelswould change. (Renal losses need to be consideredas well, but they are a relatively minor part oftheoverall balance and will be neglected for discussionpurposes, as the general concept remains thesame in any case.) Ifthe sodium influx rate nowdecreases by 10% due to exposure to silver, thenefflux exceeds influx and plasma sodium levelswill begin to decline. But the efflux is to a verygood approximation proportional to the plasmasodium level, so once the plasma sodium concentrationdecreases by 10% influx and efflux areagain in balance, though at a new equilibriumplasma sodium concentration, and the decline ofplasma sodium levels is arrested. The data ofFig.5c and d illustrate that this in fact occurs, andwhile the model is useful in explaining why thisoccurs, in hindsight, this result seems obvious.An interesting consequence to this line ofreasoningis that if30% loss ofplasma sodium isrequired for death to occur, then at least 30%inhibition ofactive uptake is required for lethality,in the absence ofdamage to the gill that mightincrease the gill permeability. Note that for thehigh chloride tests, the model correctly predictedsurvival in the NaCl treatment, the reason beingthat only approximately 5% inhibition of JMwaspredicted. Similarly, only 10% inhibition was predictedin the high KCl treatment, so survival waspredicted in this case as well, even though halfofthe fish were somewhat uncooperative in thisregard. Another limitation ofthe model, besidesfailure to be accurate in all instances, is that while


334 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343the model predicts a leveling off at a new equilibriumconcentration, the fish will not necessarilydo the same. A variety ofacclimatory responsesmay intercede, leading to longer-term recovery inthe most favorable of circumstances. For example,McDonald (1983b) has shown that at low rates ofqNa loss there is an enhanced opportunity forhormonal adjustments to take effect, reducing gillpermeability and increasing active uptake ofsodium,leading to an improved chance ofsurvival.The results ofZadunaisky (1997) suggest that theshorter-term response is stimulated by the initialchange in plasma osmolality while the longer-termresponse is more likely related to the release ofcortisone by the fish.What exactly happened in the case ofDavies’early experiments is at this point unclear. However,the results ofmore recent long-term data suggestthat water chemistry will continue to be an importantfactor in assessing silver availability and longtermeffects (Davies, 1997). Further, ongoingstudies that are directed at gaining an improvedunderstanding ofthese early results will hopefullyshed some light on this matter. Initial results withfathead minnow have indicated that losses ofsodium continue to be an important biomarker ofadverse effects leading to death (Stubblefield etal., 2000). In this regard, the SBM highlights theimportance ofchemistry not only to metal bioavailability,but to the physiological status oftheorganism itself, especially with regard to its abilityto regulate internal levels ofsodium, chloride, andperhaps other ions as well.4.3. Other considerationsWhile the capability to predict effects associatedwith alternative exposure durations is a usefulfeature of this model, it also has applicability toother aspects that are oftoxicological interest aswell. That is, this same framework should also beuseful in the interpretation and analysis of timevariable exposures, residual effects followingexposure to metals, potential effects of chlorideand other ions, and species and genus sensitivity.It may also have implications to consider fortoxicity models that have been proposed for othertypes ofchemical stressors.4.3.1. Time variable exposure and residual aftereffectsThe inhibition ofNKA activity that results fromexposure to silver has been observed to occur in adose-dependent manner (Hussain et al., 1994;Morgan et al., 1997). Further, the inhibition ofqybranchial Na and Cl influxes occurs almostimmediately upon exposure, while the effect onthe corresponding effluxes is much less (Morganet al., 1997). The speed ofthe response is consistentwith the reported rapid inhibition ofNKA byboth silver and mercury (Anner et al., 1992;Hussain et al., 1994). Further, Hussain et al.(1994), working in vitro, showed that the inhibitionofNKA activity is both rapid and reversible,while Morgan et al. (1997) showed that when theconcentration ofsilver was returned to backgroundlevels after 48 h of exposure at 2 mgyl, the sodiuminflux and net flux were almost immediatelyreturned to control values. Collectively theseresults, especially the idea that NKA inhibition israpid and reversible, provide a basis for simulatingthe effects of time variable exposures. That is, allthat is required is to reinitialize the plasma sodiumconcentration and the associated sodium fluxeseach time the silver concentration or other waterquality characteristics change, recompute BL:Agand J i, and continue to calculate the plasma sodiumconcentration over time until either the criticalplasma sodium level associated with lethalityoccurs, or recovery occurs.Fig. 9 illustrates use ofthe model to simulatetime variable effects. The situation is quite simple.The simulation begins with a pre-exposure period(t-0), during which time influx and efflux are inequilibrium and plasma sodium levels remain constant.This is followed by a 12-h exposure to themetal (0-t-12 h), and then a return to preexposureconditions (beginning at ts12 h). Thecomputations assume that NKA inhibition occursboth rapidly and reversibly, such that active sodiumuptake recovers immediately when exposure to themetal is ended. Active sodium uptake is inhibitedat the start ofthe exposure, and hence a period ofnet loss ensues and plasma sodium decreases. Atts12 h the exposure to silver is removed, activeuptake returns to normal and, as indicted by theupper dashed line, the model predicts a recoveryofplasma sodium levels over time, in the directionofpre-exposure levels. For the second case (lowercurve) it is assumed that the exposure concentrationis high enough to result in both inhibition ofactive sodium uptake plus physical damage to thegill. The gill damage is manifested in terms of anincrease in gill permeability such that P G)PGo.Inthis case, once the exposure is removed after 12


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343335Fig. 9. Illustrative model results that show how delayed effects may occur even after exposure to a metal is eliminated. The computationsassume that active sodium uptake recovers immediately, while the increased gill permeability, resulting from physical damage to thegill due caused by a short-term pulse exposure, does not recover immediately, once the metal exposure is eliminated. The upper lineshows model prediction in the absence ofgill damage, with plasma sodium beginning to return to pre-exposure levels. The lower lineshows how plasma sodium levels may continue to decrease even with uptake returned to normal, because the permeability ofthedamaged gill remains elevated. Lethality ensues at 30% depletion, some time after the exposure was eliminated.h, active uptake returns to normal, but the effluxremains elevated. As a result, sodium losses continueover time, although at a slower rate thanduring the exposure period (the lower curve att)12, where influx is returned to normal). Withplasma sodium levels continuing to decline, lethalityensues at the point of30% depletion ofplasmasodium, approximately 12 h after the exposure waseliminated. Note that these short duration simulationsdo not reflect the possible mitigating effectsthat longer-term acclimation may have, such aschanges in chloride cell density, active uptake rate,or reduced gill permeability. Such changes mayhave important implications, but they have not yetbeen incorporated in the model.4.3.2. Effect of chlorideAs noted previously, exposure to some metals,including silver and copper, may inhibit not onlysodium uptake but chloride uptake as well (Wilsonand Taylor, 1993a; Morgan et al., 1997). Thus, itis of interest to speculate about the potential effectofthe ambient chloride concentration on metalq yeffect levels. In the case of Ag , Cl reduces itstoxicity by forming the relatively non-bioavailableAgCl complex, concurrently reducing the level ofqAg and hence its degree ofinteraction at thebiotic ligand. For copper, this would not be an2qimportant factor because Cu does not form astrong chloro-complex. Aside from its effect onspeciation, it seems reasonable to speculate thatchloride may have further effects, in the case ofeither metal. Consider that active chloride uptakeoccurs in much the same way as active sodiumuptake, conforming to saturation kinetics and havinga characteristic maximum uptake rate and halfsaturation concentration for chloride in the ambientwater (Goss and Wood, 1990a,b). Also, since it isthe loss of ions from the blood via passive diffusionthat causes osmoregulatory disruption, leadingto shifts in fluids between internal compartments,ultimately leading to cardiovascular collapse anddeath, it would be expected that both sodium andchloride would play a similar roll. Ifso, it followsthat anything, which affects chloride regulation,will have a bearing on the response ofthe organism.Because relatively high chloride levels in theambient water will facilitate the active uptake ofchloride, this would be expected to reduce the rateofany net loss rate ofchloride that occurs whenactive uptake has been inhibited or, under relativelyextreme conditions, where efflux has increased


336 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343due to an increase in gill permeability. This effectshould occur not only for silver but for copper aswell. In fact, recent test results with Daphnia sp.have shown that the Cu LC50 values did in factincrease with an increase in chloride levels in thetest water (Rodriguez et al., 2001).Another effect of increasing the chloride levelin the ambient water would be to reduce theconcentration gradient between the blood andwater and hence diffusive losses. This wouldnormally be expected to be a relatively slighteffect in freshwater settings, however, becauseambient chloride levels remain low, typically inthe range of0.05–5 mM (approximately 2–200mgyl), in comparison to plasma chloride levels ofapproximately 150 mM (5250 mgyl). However,Lewis and Lewis (1971), in tests with channelcatfish and golden shiner, showed that increasingthe concentration ofNaCl in the ambient water tolevels approaching the osmolality ofthe blood,actually mitigated the adverse effects of exposureto Cu. While both sodium and chloride levels wereincreased in this case, it was necessary that theybe increased to levels well in excess ofwhereactive uptake is saturated in order to preventqeffects. It follows that at this level of Na andyCl in the ambient, the diffusive losses would bemarkedly reduced, thereby mitigating what wouldotherwise be the expected acute effects of exposureto copper. Several other examples have beenreported where elevated levels ofsodium in theambient water affected the diffusive flux of ionsbetween the water and plasma. Wilson and Taylor(1993b) showed how plasma sodium levels ofrainbow trout exposed to copper in saltwaterincreased (the direction of the diffusion gradientis reversed in saltwater) until internal and externallevels ofsodium were about equal. Packer andDunson, in low pH exposures, also showed howelevated sodium levels extended survival timefrom 2 to 8 h, though death eventually ensued,probably as a result oflosses ofother ions. It isexpected that elevated external chloride levelswould have a similar beneficial effect, at least inregard to reducing diffusive losses from the blood.Chloride uptake could be readily incorporated intothe IBM model framework. If warranted, ionspecificgill permeability coefficients (Potts, 1984)could also be included. Potts (1984) presents theequations that describe the fluxes associated withthese electrochemical gradients, should furtherrefinement be needed.4.3.3. Species sensitivityThe reason for differences in species sensitivityto various chemical stressors, including metals, isnot well known. McDonald et al., in an effort tounderstand why these differences exist for fish,conducted a study of the differences in gill morphologyof freshwater fish in relation to theirsensitivity to low pH conditions (McDonald et al.,1991). On the basis ofparallel studies with bandedsunfish, yellow perch, smallmouth bass, rainbowtrout and common shiner (listed in order oflowestto highest sensitivity to pH and spanning the limitsof resistance to pH effects among freshwater teleosts),they concluded that acid tolerance is notcorrelated with some ofthe basic physical dimensionsofthe gills (surface area, thickness or blood–water diffusion distance) or with the degree ofmucous formation on the surface (i.e. the ‘degreeof mucification of the surface’). However, theyfound that it may be correlated to the chloride celldensity and the branchial ion-transport activity.They interpreted this to indicate that sensitivity tolow pH is related to the intrinsic ion-permeabilityofthe gills, which is related to the depth ofthetight junctions between adjacent gill pavementcells.The observation ofMcDonald et al. (1991) thatthe chloride cell density increased with increasingsensitivity may at first seem counterintuitive, sincea high transport capacity would seem to be apositive attribute. This is in fact a reasonable resultif viewed from a different perspective. That is, thetendency for the more sensitive fish species topossess higher chloride cell densities is due to thefact that their gill epithelium is relatively permeable(i.e. ‘leaky’). This in turn requires that theypossess a relatively high chloride cell density andan associated high JMto increase their ionic uptakecapacity, a necessity for maintaining homeostasiswith regard to the ionic composition oftheirintracellular fluids.Incorporation ofthe key physiological featuresof sodium uptake and efflux in the SBM makes itwell suited for the analysis of species sensitivityin a way that considers the preceding mechanisms.A thought experiment will be used to illustratehow these characteristics would explain speciessensitivity in the context ofthe SBM. First, inorder to maintain simplicity without loss ofgenerality,neglect renal losses. Next, consider twofish species that have the same plasma sodiumconcentration, but one has a low sodium influx


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343337rate and the other a relatively high influx rate (e.g.Jis4 and 8 mmolykgwyd). Consistent with theneed to maintain intracellular homeostasis, it canbe estimated from Eq. (7) that the gill permeabilitymust be higher (i.e. the gill is ‘iono-leakier’) forthe species with the higher uptake rate. Moredirectly, the effluxes for the two species will be 4and 8 mmolykg yd, equal to the respective influxwes, for equilibrium conditions to be maintainedwith respect to plasma sodium. Ifit is assumedthat the differences in sodium uptake rates vary inaccordance with NKA activity, and that exposureto silver in the same test chamber will result inthe same biotic ligand concentration for each fishspecies (the biotic ligand and binding constant arethe same in each case), then the percent inhibitionofsodium uptake will also be the same (Fig. 6).Assuming 75% inhibition occurs for this example,then the net loss ofsodium will be JiyJes2y8sy6 mmolykg yd in the one case and J yJ sw i e1y4sy3 mmolykg yd in the other case. Allwother things equal, the fish with the higher net rateofloss will lose 30% ofits exchangeable sodium(7.5 mmolykg ifthe exchangeable pool is 50wmmolykg ) in 1.25 days while the less sensitivewfish with the lower rate of loss will survive for2.5 days. Alternatively, it is readily shown thatonly 37.5% inhibition is required for a survivaltime of2.5 days for the more sensitive species,the one with the higher efflux rate, so the LC50would be lower as well, given the same exposurewater characteristics.It should be understood that there is somewhatofa ‘chicken or the egg’ conundrum here, as it isnot perfectly clear what is the more fundamentalparameter that leads to an organism being sensitiveto exposure to metals, the high uptake rate or thehigh loss rate ofsodium and other ions. While ahigh uptake rate in combination with a fixedexchangeable sodium pool is associated with afaster response time when an organism is stressedthan is a slow uptake rate, it is not clear that it isthe uptake rate per se that is causally related tothe response time. Rather, the capability to efficientlytake up sodium at a relatively high rate ismore likely to be an asset, a capability that hasdeveloped, perhaps evolved, from the need toovercome the high rate ofloss ofsodium associatedwith a leaky branchial epithelium. Further,considering that this is an energy demanding process,it is not an energetically advantageous processthat an organism would be likely to carry out,except out of necessity. The efflux rate is morelogically expected to be the cause ofa shortresponse time, as once the uptake is reduced orentirely eliminated, it is the efflux alone thatcontrols how quickly the steady state sodium poolwill decrease in concentration. Regardless ofwhatlogic and intuition might offer in answering thisproblem, the insight provided by the mathematicalsolution to the problem is that it is the efflux rateofsodium that controls the response time, ratherthan the influx rate. The ratio of the uptake toefflux rates will control the magnitude of thesteady state plasma sodium concentration, but onlythe efflux rate, including both passive losses at thegill and renal losses, will control the response timeof the organism to exhibit effects due to inhibitionofthe active uptake system. At the same time,perhaps there are some inherent metabolic advantagesto a high sodium uptake rate, perhaps relatedto the need to maintain acid–base homeostasis inconjunction with high metabolic needs. Ifso, theremay be a compensatory advantage, an underlyingneed for some organisms to possess a higher effluxrate ofsodium than others. Recent investigationssuggest that this need may derive from energeticrequirements that are related to organism size(Bianchini et al., 2002; Grosell et al., 2002). Theeffect of size on sodium uptake rate could beadded to the model via a simple regression equationthat relates sodium uptake rate to size, or bysimply estimating the uptake rate independent ofthe model and setting the appropriate value as amodel input.Finally, it is ofinterest to consider a comprehensivesummary ofdata on osmo-conformers andosmo-regulators that has been compiled by Manteland Farmer (1983). In view ofthe results thathave been presented above, review ofthese databegs the question ofwhether or not osmo-conformers,aquatic organisms who’s plasma osmolalitytends to vary with the ambient, would tend to havea reduced sensitivity to metals, since the lowconcentration gradient would reduce the efflux andhence the rate ofchange in plasma compositionthat arises from diffusive losses or gains.5. SummaryThe model described herein provides a uniquebasis for considering the effects of metals onionoregulation by aquatic organisms. Thoughdeveloped for fish exposed to silver, the same type


338 P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343offramework should be readily adaptable to othertypes oforganisms, including invertebrates, and toother metals as well. Ofcourse, an understandingofthe underlying physiological mechanisms wouldbe a pre-requisite to the successful application ofthe model. At the same time use ofthis type ofmodel should help to elucidate the significance ofthese underlying mechanisms. By incorporating adirect link to the BLM ofthe acute toxicity ofmetals, the SBM extends the utility ofthisapproach in a number ofways. While the focus ofthe BLM is on the chemical interactions ofwaterquality characteristics on metal availability andtoxicity, the SBM adds an additional dimension,focusing on the physiological interactions of waterquality characteristics with the organism itself.With regard to calcium, Playle et al. showedthat it was not protective ofgill Ag accumulation,a result that is consistent with toxicity data that2qshow that Ca (and hardness generally) does noteffectively compete against silver to mitigate theinhibition ofsodium uptake that is caused bysilver. Here, we see that at high silver concentrations,where physical damage to the gill is believed2qto have occurred, Ca appears to be protective ina different way, by maintaining the integrity of thegill structure, specifically the calcareous paracellularjunctions.yAn equimolar concentration ofCl is even more2qprotective than Ca at the elevated silver levelsconsidered herein, not only because it reduces freesilver, thereby reducing the inhibition ofactivesodium uptake, but because the decrease in freesilver is also protective ofthe physical integrity ofthe gill. Comparison ofthe results ofexperimentswith additions ofKCl compared to NaCl showsqthat Na is also beneficial to the organism. In thecontext ofthe BLM this benefit is a competitiveone, resulting in reduced inhibition ofsodiumuptake kinetics, while in the SBM, there are twoadditional benefits of increased levels of sodiumin the external water. These are the enhanceduptake ofsodium via the carrier-mediated uptakesystem and, to a lesser degree, a decrease indiffusive losses due to a decrease in the plasma–water concentration gradient that controls diffusivelosses.Finally, while the mechanism is not currentlyincluded in the model, the conceptual frameworksuggests, by analogy to sodium, that elevatedchloride levels may have additional physiologicalbenefits to aquatic organisms. That is, an increasein the level ofchloride would be expected tofacilitate chloride uptake via the carrier-mediateduptake system and, to a limited degree in thestudies considered herein, it would also decreasethe blood–water concentration gradient ofchloride,thereby reducing diffusive losses of chloride.One ofthe interesting insights that the SBMoffers is that two very different dissolved LC50values can have the same time to death and thecritical accumulation level at the biotic ligand,need not be uniquely defined. This finding iscounter to one ofthe underlying premises oftheBLM that the LA50 value associated with a fixedeffect is invariant. The reason this may occur isthat there are other non-stressor related waterqquality characteristics (e.g. the Na concentrationin the water) which may affect the ability of theorganism to survive through a direct effect of ametal on the physiological status ofthe organismq(e.g. Na uptake kinetics), without necessarilyinteracting with the metal at the site ofaction oftoxicity. To date, although such effects have beensuccessfully subsumed within the guise of thechemical interactions incorporated in the BLM,they are in fact significant physiological interactionsthat may, as an alternative, be treated explicitlywithin the context ofthe SBM. While addingto the complexity ofthe overall analysis, byconsidering these interactions in this manner thepotential utility ofthe BLM is enhanced.While to some degree the conditions oftheexperiments that were analyzed herein made itpossible to distinguish between the chemical andphysiologically processes that concurrently affectmetal availability and biological effects, this distinctionwas not totally unambiguous. Among thethings that will be needed in the future will beexperiments that are designed to clearly differentiatebetween those effects that are chemical innature, as are currently represented in the BLM2q q(e.g. competition ofCa or Na with the metalat the biotic ligand), and those that are morephysiological in nature, as exemplified in the SBM2qq(e.g. effects of Ca on permeability and Na onuptake kinetics). The chemical factors serve toreduce metal availability and provide a first lineof defense for the organism, one that prevents themanifestation of effects in the first place, whilethe physiological factors alter the sensitivity of theorganism to the adverse effects of elevated concentrationsofmetals, when they are manifested.In the interim, the BLM ofacute toxicity subsumes


P.R. Paquin et al. / Comparative Biochemistry and Physiology Part C 133 (2002) 305–343339these concurrent chemical and physiological processesand related effects into the chemical interactionsthat are represented in the model. The factthat it does this may account for some of theresidual uncertainty in BLM predictions, uncertaintythat will ultimately be able to be reduced, or asa minimum better understood, by further considerationofthe physiological interactions that takeplace.It will also be ofutmost importance in the futureto gain an improved understanding ofthe processesthat are involved in acclimation ofthe test organisms,both in the laboratory and the field, and tointroduce these processes into the model framework.This will be ofparticular utility in helpingto understand chronic effects that result from longterm,low-level exposures to metals. While notcurrently included in the model frameworkdescribed herein, it is envisioned that the effectsq y yofpH on Na uptake, and HCO3on Cl uptakeare additional refinements that will enhance theapplicability ofthe model and serve to furtherelucidate the importance ofthe interactions ofthemany chemical and physiological processes ofimportance. Incorporation ofosmoregulatory processesthat control internal fluid transfers may alsobe ofuse.The demonstrated capability ofthe IBMySBMframework to predict survival time under alternativeexposure conditions is a useful feature of thisphysiologically-based framework. However, perhapsofeven greater importance is its potentialfuture utility as a framework for analyzing theeffects of time variable exposure conditions, residualafter-effects of exposure to metals, acclimation,chronic toxicity and species and genus sensitivity.The development ofa predictive model thatincludes each ofthese capabilities will requirefurther refinements and a concerted, collaborativeeffort by chemists, physiologists toxicologists andmodelers alike. However, this type ofmodel shouldbe ofgreat value to regulatory agencies that needto consider species sensitivity distributions foracute and chronic toxicity, and the magnitude,frequency and duration of exceedances in developingrefined WQC for metals. These same featureswill also provide the risk manager with animproved tool for use in making risk managementdecisions with respect to the assessment oftheexpected effects of metals in aquatic settings.AcknowledgmentsThis work was completed with the financialsupport ofthe Eastman Kodak Company, Rochester,NY and the International Imaging IndustryAssociation, Harrison, NY. The helpful comments,support and assistance ofMr Joseph Gorsuch ofEastman Kodak Company and two anonymousreviewers are also gratefully acknowledged.ReferencesAllen, H.E., Hall, R.H., Brisbin, T.D., 1980. Metal speciation,effects on aquatic toxicity. Environ. Sci. Technol. 14, 441.Allen, H.E., Hansen, D.L., 1996. The importance oftracemetal speciation to water quality criteria. Water Environ.Res. 68, 42–54.Anderson, D.M., Morel, F.M.M., March 1978. Copper sensitivityofGonyaulax tamarensis. Limnol. Oceanogr. 23,283–295.Anner, B.M., Moosmayer, M., Imesch, E., 1992. 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