Computational modelling of amino acid transfer interactions in the placenta

Transcription

1 Exp Physiol 95.7 pp Experiental Physiology Research Paper Coputational odelling of aino acid transfer interactions in the placenta B. G. Sengers 1,C.P.Please 2 andr.m.lewis 3 1 Bioengineering Research Group, School of Engineering Sciences, University of Southapton, UK 2 School of Matheatics, University of Southapton, UK 3 Developental Origins of Health and Disease, School of Medicine, University of Southapton, UK Aino acid transfer fro other to fetus via the placenta plays a critical role in noral developent, and restricted transfer is associated with fetal growth restriction. Placental aino acid transfer involves the interaction of 15 or ore transporters and 20 aino acids. This coplexity eans that knowing which transporters are present is not sufficient to predict how they operate together as a syste. Therefore, in order to investigate how placental aino acid transfer occurs as a syste, an integrated atheatical/coputational odelling fraework was developed to represent the siultaneous transport of ultiple aino acids. The approach was based on a copartental odel, in which separate aternal, syncytiotrophoblast and fetal volues were distinguished, and transporters were odelled on the aternal- and fetal-facing ebranes of the syncytiotrophoblast using Michaelis Menten-type kinetics. The odel was tested in coparison with placental perfusion experients studying serine alanine exchange and found to correspond well. The results deonstrated how the different transporters can work together as an integrated syste and allowed their relative iportance to be assessed. Placental fetal serine exchange was found to be ost sensitive to basal ebrane transporter characteristics, but a range of secondary, less intuitive effects were also revealed. While this work only addressed a relatively siple three aino acid syste, it deonstrates the feasibility of the approach and could be extended to incorporate additional experiental paraeters. Ultiately, this approach will allow physiological siulations of aino acid transfer. This will enhance our understanding of these coplex systes and placental function in health and disease. Received 18 February 2010; accepted after revision 21 April 2010; first published online 23 April 2010) Corresponding author B. G. Sengers: Bioengineering Research Group, Eustice Building 5, University of Southapton, Southapton SO17 1BJ, UK. Eail: braseng@soton.ac.uk Aino acid transport fro other to fetus via the placenta is a critical deterinant of fetal growth, and restricted aino acid transfer has been associated with ipaired fetal growth Paoliniet al. 2001). Not only is the overall quantity of essential and non-essential aino acids transported iportant, but also the relative quantities of specific aino acids. In the healthy placenta, these fetal requireents are et via a highly coplex array of active transport and facilitated exchange echaniss Cleal & Lewis, 2008). In the huan placenta, the aternal blood perfuses the intervillous space in direct contact with the fetal villi. Separating the aternal and fetal blood are a series of cellular and connective tissues layers, the syncytiotrophoblast, followed by discontinuous layer of cytotrophoblast, stroal connective tissue and finally the fetal capillary endotheliu. The syncytiotrophoblast fors a continuous barrier around the villi and is the priary barrier preventing transfer of solutes across the placenta. The fetal capillary endotheliu contains spaces between the endothelial cells that allow the diffusion of sall solutes. At the end of the second triester and in the third triester, dilatation of the capillaries within the villi takes place, bringing the into close contact with the syncytiotrophoblast and increasing the efficiency of nutrient transfer Castellucci & Kaufann, 2006). Overall, aino acid transfer across the placenta is an active process, with aino acid concentrations in fetal plasa being higher than in aternal plasa Cleal & Lewis, 2008). Aino acids first cross the aternal-facing icrovillous ebrane MVM) to be DOI: /expphysiol

2 830 B. G. Sengers and others Exp Physiol 95.7 pp taken up in the ultinucleated cell layer that fors the syncytiotrophoblast, fro where they can cross the fetal-facing basal ebrane BM) into the fetal circulation Fig. 1). Accuulative transporters in the cell ebrane actively transport aino acids into the syncytiotrophoblast fro both aternal and fetal sides. Aino acid exchangers change the relative coposition of aino acids but cannot change the overall aount. Additional echaniss are therefore required to obtain the net transfer of aino acids necessary to support fetal growth, since accuulative transporters in the BM cannot ediate efflux of aino acids fro the placenta and exchangers only affect the relative aino acid coposition and not the quantity. Indeed, we have recently deonstrated the existence of additional efflux transporters in the BM Cleal et al. 2007; Cleal & Lewis, 2008). Another iportant coponent of placental transfer is paracellular diffusion, i.e. bypassing the cells of the syncytiotrophoblast. While it is clear that this does occur in the placentae of any species, the echaniss are not well understood, as reviewed by Sibley 2009). To study these exchange echaniss in detail we have previously eployed an ex vivo perfusion set-up, in which aino acid transfer in isolated huan placentae can be deterined in the absence and presence of certain aino acids Cleal et al. 2007). Furtherore, by introducing a bolus of a specific aino acid into the fetal circulation an exchange response is triggered, resulting in the teporary release of specific other aino acids, which can be used to work out the echaniss responsible. However, given the coplexity of these coupled transport echaniss and the variety of possible interactions between different copeting aino acids and exchange echaniss, an enhanced quantified insight into placental aino acid transfer at the syste level is urgently needed. Matheatical/coputational odelling is ideally suited to describe and provide insight in these types of coplex coupled phenoena. Most odelling studies in the past have focused ainly on blood flow, water exchange or oxygen and carbon dioxide transfer between other and fetus Wilbur et al. 1978; Schröder, 1982; Grooe, 1991; Sebire et al. 2004). Models have either evaluated spatial flow patterns Erian et al. 1977; Schid- Schönbein, 1988) or focused on the scale of a single capillary Guilbeau et al. 1973; Costa et al. 1992). An excellent coprehensive overview of these odelling approaches has been copiled by Chernyavsky et al. 2010). In an early study, the effect of aino acids, aong other solutes, on water exchange in the placenta has been included by pooling all aino acids together and assuing that active uptake on the aternal side leads to a high constant level within the placental tissue, fro where the aino acids diffuse passively into the fetal circulation Wilbur et al. 1978). For flow, the pulse propagation in arterial placental networks has been odelled to investigate the blood supply in onochorionic twin pregnancies and the effect of the tiing of the fetal heart beats Franke et al. 2003). In addition, factors such as viscoelastic arteries, the effect of elastin on blood vessel copliance and blood haeatocrit dynaics have been included van den Wijngaard et al. 2007). Furtherore, recently, atheatical odelling was applied to study the effect of the aternal flow configuration in and out of the placenta on generalized nutrient uptake efficiency, with the intervillous space odelled as a hoogeneous porous ediu Chernyavsky et al. 2010). However, while these approaches could account for flow or nutrient/oxygen uptake in general, none of these previous odels has specifically addressed the highly coplex aino acid transfer syste. Therefore, the objective of the present study was to develop a coputational odelling fraework specifically for aino acid transport in the placenta, which is able to represent and provide quantitative insight into the coplex interactions that occur during the exchange of ultiple aino acids. Previous studies by ourselves and others have identified ebrane transporter echaniss and led to the establishent of a conceptual description of placental aino acid transfer in the huan placenta Cleal & Lewis, 2008). In the present study, these echaniss were translated into coputational odelling relationships and assuptions for transporter kinetics, which enabled us to construct an integrated odel of the transport of ultiple aino acids. Both the validity of these assuptions and the ability of the odelling fraework as a whole were subsequently tested in coparison with experiental data fro our previous aino acid infusion experients on serine alanine exchange Cleal et al. 2007). Methods All experiental data used are fro our previous study Cleal et al. 2007). Placentae were collected with written infored consent and with approval of the South and West Hapshire Local Research Ethics Coittee. Copartental odel definition As a first approach, a relatively siple copartental odel was developed to describe aino acid transfer in the placenta. This luped odel only described overall exchange and did not account explicitly for specific geoetric features. The advantage of this approach was that it significantly reduced the nuber of paraeters involved. Three copartents were distinguished in the odel: aternal, syncytiotrophoblast and fetal, denoted by the subscripts, s and f, respectively Fig. 1A and B).

3 Exp Physiol 95.7 pp Modelling placental aino acid transfer 831 As a first assuption, each of these copartents was considered well ixed. Thus, each of these copartents is described by a defined volue containing a set of different aino acids at certain concentrations. Over tie these concentrations can change as a result of blood perfusion and aino acid transfer between the three copartents, which is governed by the different exchange and transport echaniss. Thus, aino acid transfer in general is given by: dc i dt dc i f dt = 1 v Q i,perf Q i s Q i f dc i s dt = 1 Q i s v Q ) i sf s = 1 v f Q i f,perf + Q i sf + Q i f ) ) 1) 2) 3) where c i k in ol 3 ) is the concentration of aino acid i in copartent k, v k in 3 )isthevolueof the copartent, Q i kl in ol s 1 ) is the net olecular flux of aino acid i fro copartent k to l,andq i k,perf in ol s 1 ) is the net influx due to perfusion. Aino acid etabolis in the syncytiotrophoblast was not considered in the present study; therefore, no additional source ter appears in eqn 2). Since the priary goal was to study aino acid transfer interactions, as a first approach highly siplified, largely phenoenological relationships were adopted to describe the functional features of the transporter kinetics. Hence the fluxes Q in eqns 1 3) will be found as cobinations of the contribution of the following types of transport that were distinguished in the odel. Accuulative transporters Accuulative transporters e.g. syste A) in the MVM and BM actively transport aino acids into the syncytiotrophoblast fro either the aternal or the fetal side. It was assued that each transporter has a axial capacity Vacc ax in ol s 1 2 ), which is shared between copeting aino acids. For siplicity and to reduce the nuber of paraeters involved, it was first assued that the transporter follows a Michaelis Menten-type relationship and has the sae affinity for all aino acids it acts upon. This siply iplies that the aino acids are transported according to their relative concentration fractions, for exaple in the MVM: Q tot acc = A totv ax acc Q i s,acc = Q tot c i acc K acc + ; Nacc = c i i=1 4) Here Q tot acc in ol s 1 ) is the total olecular flux fro the aternal into the syncytiotrophoblast copartent for this transporter, and A tot in 2 ) the exchange area. The value of Q tot acc is effectively deterined by external aino acid availability via the total concentration of aternal aino acids in ol 3 ), which is the su of all the aino acids c i, i = 1...N acc, the transporter acts upon. The Michaelis Menten constant K acc in ol 3 ) is the concentration at which the half-axial transfer rate occurs. The flux Q i s,acc is the fraction of the total olecular flux that consists of a specific aino acid i,and this then dictates the rate of concentration change in the aternal and syncytiotrophoblast copartents and s, according to the ass balance eqns 1) and 2)) The sae Figure 1. Placental aino acid transport A, conceptual overview of aino acid transfer in the placenta showing the location of the different accuulative transporters syste A) and exchangers LAT2 and ASCT1/2) applicable to serine alanine exchange Table 1; Cleal & Lewis, 2008). MVM is the icrovillous ebrane and BM the basal ebrane. Note that for these aino acids no efflux transporter in the BM applies. B, copartental coputational odel, in which a aternal, syncytiotrophoblast s and fetal f copartent are distinguished. Each copartent k is defined by a volue v k and different aino acid concentrations ck i. The aino acid flux between the copartents k and l is denoted by Q kl,andf perf k is the aternal and fetal flow with inlet concentration c ink.

4 832 B. G. Sengers and others Exp Physiol 95.7 pp expressions apply for accuulative transporters in the BM fro the fetal to syncytiotrophoblast copartent, denoted accordingly by the subscripts f and s. Exchange transporters Aino acid exchangers [e.g. The Syste L aino acid exchanger LAT2) and the Syste ASC aino acid exchanger ASCT2)] in the MVM or BM can alter the relative coposition but not the absolute aount of aino acids. Aino acids are exchanged on a one-forone basis and therefore in the odel the olecular flux in one direction across the ebrane is equal to the flux in the opposite direction. For exchange to occur, the appropriate aino acids need to be present at each side of the ebrane. Thus, in the odel the total flux is liited by the aino acid availability on either side of the ebrane. To incorporate this restriction it was assued that the flux is given by the product of two Michaelis Menten expressions, one for the total external concentration of aino acids and one for the total internal concentration of aino acids on which the transporter acts; for exaple in the MVM: Q tot exc = A totv ax exc c i ; = Nexc i=1 Q i s,exc = Q tot exc c i K exc + c N exc tot s = c i s s c i s i=1 ) ) s K exc + s ) ; 5) Where Q tot exc in ol s 1 ) is the total olecular flux in one direction, Vexc ax in ol 2 s 1 ) the axial exchange rate and K exc in ol 3 ) the Michaelis Menten constant, which was assued to be equal for all aino acids, as well as equal for transport in either direction across the ebrane. Specific aino acids c i are exchanged with net flux Q i s,exc according to their relative fractions on the aternal ) and syncytiotrophoblast s) side. For exaple, if a certain aino acid akes up 100% of aino acids outside the syncytiotrophoblast and 50% inside then exchange will result in a net transfer into the syncytiotrophoblast. With the appropriate subscripts, s and f, the sae expressions apply for transport through the BM between syncytiotrophoblast and fetal circulation. Both accuulative transporters and exchangers can be present in the ebrane; therefore, in general, Q i kl = Q i kl,acc + Q i kl,exc in eqns 1 3). Paracellular transport In previous studies, a baseline level of solute transfer fro the aternal to the fetal side was deonstrated using arkers creatinine) that are neither actively transported nor exchanged and taken up into the cells of the syncytiotrophoblast Cleal et al. 2007). While the nature of the paracellular route is not fully understood, it is likely that it represents passive diffusion through fibrin-containing clots over areas of daaged syncytiotrophoblast Brownbill et al. 2000; Sibley, 2009). In the odel eqns 1) and 3) this echanis was represented with a siple diffusion relationship, which applies non-specifically to all aino acids: Q i f = PA tot c i c i f ) 6) Where Q i f in ol s 1 ) is the olecular flux of aino acid i directly fro the aternal to the fetal copartent, bypassing the syncytiotrophoblast and thus independent of c i s ), and P in s 1 ) is the effective diffusion rate. Note that instantaneous steady diffusion was assued, based on the short paracellular diffusion distance between capillary and intervillous space. Perfusion flow In the experient Cleal et al. 2007), the aternal and fetal copartent were perfused at different flow rates with balanced salt solutions suppleented with aino acids at certain defined concentrations. The change in concentration due to the flow in and out of the placental copartent is then given by: Q i,perf = F perf c i in, c i ) 7) Where Q i,perf in ol s 1 ) is the net olecular flux, F perf in 3 s 1 ) the perfusion flow rate and c i in, is the inlet aino acid concentration of a specific aino acid i. The sae expression applies to the flow in the fetal copartent. This then copletes the definition of the separate ters Q in the three copartent odel eqns 1 3)). Nuerical ipleentation The aino acid transfer odel as outlined above was ipleented using Matlab version 7.9.0, The Mathworks, Natick, MA, USA). Briefly, the three copartent odel eqns 1) 3)) yields a syste of coupled non-linear ordinary differential equations. For siplicity, a standard explicit Euler tie integration schee was adopted to solve this set of equations. Tie steps were refined until further refineent yielded no significant iproveent in accuracy of the solution 2500 tie steps of 3.5 s each). Note that ore efficient integration schees could be eployed to save coputation tie; however, this was presently not an issue.

5 Exp Physiol 95.7 pp Modelling placental aino acid transfer 833 Table 1. Transporter localization and substrate specificity within the odel Transport specificity Localization in the Radiolabelled Transport placental Serine serine Alanine Glycine Transporter type syncytiotrophoblast Syste A Accuulative MVM BM LAT2 Exchange MVM ASCT1/2 Exchange BM Paracellular diffusion Not applicable MVM is the icrovillous ebrane and BM the basal ebrane. +/ denotes whether or not the aino acid is a substrate of the transporter. Glycine is a low-affinity substrate of Syste L aino acid exchanger LAT2) and was not regarded as a substrate within the odel. ASCT1/2 represents both the Syste ASC aino acid exchangers ASCT1 and ASCT2. Proble definition The odel was first applied to analyse the exchange of serine and alanine based on our previous experients. The experiental procedure has been described in detail by Cleal et al. 2007). Briefly, placentae were collected fro noral pregnancies iediately after delivery. The experient was repeated for a total of five different placentae. First, both the aternal and the fetal sides were perfused with a odified Earle s bicarbonate buffer EBB). After in, the aternal arterial perfusion was switched to EBB containing 100 μm of L-serine and 120 μm glycine, as well as 0.6 μm of radiolabelled L-[ 14 C]serine. Throughout the experient, the aount of tracer in both the aternal and the fetal outflow was easured by taking saples every 1 5 in. At approxiately 60 and 100 in, two separate 3 l boluses with 10 and 20 μol L-alanine injected in the fetal inflow induced a distinct serine exchange as easured by the appearance of peaks of radiolabelled serine in the fetal outflow Fig. 2A). To odel transport for this syste, we distinguish four different aino acids: serine, radiolabelled serine, alanine and glycine. Transporter localization in the odel is set out in Fig. 1A and the aino acids they act upon set out in Table 1 N acc = 4ineqn4)andN exc = 3 in eqn 5)). Accuulative transport by syste A is localized to both the MVM and the BM, and all three syste transporters with syste A-like activity SLC38A1, SLC38A2 and SLC38A4) were odelled as one generic transporter Jansson et al. 2002). The exchanger LAT2 SLC7A8) was localized to the MVM in line with our previous findings that there is syste L-like 2-ainobicyclo[2,2,1]heptane-2- carboxylic acid BCH) inhibitable) serine uptake on the MVM Lewis et al. 2007; Brand et al. 2010). Although Kudo & Boyd 2001), using BM vesicles, suggest that LAT2 is active on the BM, we do not see any evidence for this in the isolated perfused placenta, and in the odel LAT2 is not localized to the BM Cleal et al. 2007). The Syste ASC aino acid exchangers ASCT1 SLC1A4) and ASCT2 SLC1A5) were odelled as one generic transporter localized to the BM Johnson & Sith, 1988). Syste A transports all three aino acids, while ASC and LAT2 transport alanine and serine Cleal & Lewis, 2008). While glycine has been reported to be transported by huan LAT2, it is a low-affinity substrate, and it was therefore assued that glycine will not be exchanged Segawa et al. 1999; Meier et al. 2002). Model paraeters For the fetal input concentrations, the shape of the pulse resulting fro aino acid injection was easured. These Figure 2. Coparison between the odel predictions and experiental data for a representative experient investigating fetal serine release A) and aternal serine output B) The continuous line represents the odel output, while the squares and dashed line represent experiental data. Radiolabelled serine was converted to total serine based on the aternal input ratio of 0.6%, as in the experient. Arrows indicate the ties at which an alanine bolus was adinistered to the fetal circulation.

6 834 B. G. Sengers and others Exp Physiol 95.7 pp experiental values were directly used in the odel as fetal input, starting at the bolus injection ties. As in the experient, the aternal and fetal flow rates were 14 and 6 l in 1, respectively. Maternal v ), syncytiotrophoblast v s ) and fetal v f ) volues were based on a perfused cotyledon weight of 37 g siply equated to illilitres) and a relative volue of 34, 15 and 7.5% for the intervillous space, trophoblast and fetal capillaries, respectively Mayhew, 2009). It was verified that including the fetal stroa volue could not reproduce the experiental results see Results). The exchange area A tot was calculated fro the fetal volue based on a capillary cross-sectional area of 150 μ 2, corresponding to a diaeter of 14 μ Mayhew, 2009). The initial concentrations c i s0 within the syncytiotrophoblast were 721 μm for serine unlabelled), 1987μM for alanine and 1655 μm for glycine Philipps et al. 1978). Radiolabelled serine as well as all fetal and aternal concentrations were set to zero initially. Only incoplete data are available for the Michaelis Menten constants K ) of aino acid transporters. Furtherore, the present odel did not distinguish between the K of different aino acids; therefore, necessarily representative average values were selected. Constant K acc eqn 4)) for syste A was set to 320 μm for both MVM and BM, based on the K for Na + -dependent serine uptake into placental MVM vesicles Lewis et al. 2007) and the values for the Syste A aino acid transporter proteins SNAT1 and SNAT2 for alanine Mackenzie et al. 2003). For the exchanger LAT2 in the MVM, K exc eqn 5)) was set to 152 μm, based on the average of the values for alanine and serine Segawa et al. 1999). For the exchanger ASCT1/2 in the BM, the K exc eqn 5)) was set to an average of 172 μm, basedonthek for alanine for ASCT1 Pinilla et al. 2001; Pinilla-Tenas et al. 2003) and the K for glutaine for ASCT2, which has a siilar affinity to alanine and serine Kekuda et al. 1996; Wasa et al. 2002). Paraeter estiation procedure To deterine the effective transporter rates for the individual placentae, the odel was fitted to the experiental data of each of the five experients separately. Three paraeters were estiated eqns 4) 6)) as follows: i) the coefficient for paracellular diffusion P; ii) the axial exchange rate Vexc ax for ASCT1/2 in the BM; and iii) the axial uptake rate Vacc ax for syste A in the MVM. To reduce the nuber of paraeters to be estiated, the axial exchange rate Vexc ax for LAT2 in the MVM was set to 75% of Vacc ax for syste A in the MVM, based on the total and Na + -independent serine uptake in MVM vesicles Lewis et al. 2007). In addition, the effective value of Vacc ax for syste A in the BM was assued to be 6% of the value for syste A in the MVM, estiated fro the difference in total uptake in vesicle studies Jansson et al. 2002). To easure the difference between odel predictions and experiental data, the following error criterion C est was adopted: b 2 ) cop b f 2 cop C est = 1) + 1 b exp + 1 N peak N peak i peak =1 h i peak cop h i peak exp b f exp 1 ) 2 8) Here, b cop and b exp are the coputed and experiental aternal steady-state baseline, respectively Fig. 2); siilarly for the fetal baselines b f cop and bf exp.thefetal peak heights are denoted by h cop and h exp,andn peak is the nuber of peaks. This criterion was adopted, rather than coparing the raw data, since the odel could not represent the initial phase see Results section) and to reduce the sensitivity to differences in experiental peak tiing. The average aternal and fetal baselines were deterined fro the first peak onwards, excluding peaks. Experiental and coputational peak heights were deterined by subtracting their respective baselines between the values before and after the peak. Briefly, the Matlab function finsearch Nelder Mead ultidiensional unconstrained non-linear iniization) was used to estiate the set of three paraeters siultaneously by iniizing the difference between odel and experient as quantified by C est. Thus, the odel siulation of the full experient was run as a function in the estiation loop, with the three adjustable odel paraeters as input and the error criterion C est as output, and repeated until convergence was reached. Approxiate initial estiates to start the fitting procedure were deterined anually for one experient and then varied by ±50% to test the uniqueness of the fitted paraeters. In addition, a paraeter variation study was carried out in which the estiated and other odel paraeters were varied with a factor ranging fro 0.1 to 10 i.e. 0.1, 0.5, 0.9, 1.1, 2, 5 and 10), in order to evaluate the odel s sensitivity, as well as the effect on the quality of the fit for all individual experients. Physiological aino acid siulation As well as fitting the bolus experients, additional siulations were perfored to assess the odel iplications. As an initial step towards a ore physiological situation, the cobined input of all the odelled aino acids i.e. serine, alanine and glycine) was considered. In vivo concentrations were applied as constant inputs on both the aternal and the fetal side.

7 Exp Physiol 95.7 pp Modelling placental aino acid transfer 835 Maternal input serine, alanine and glycine concentrations were 93, 268 and 132 μm, respectively, while fetal input serine, alanine and glycine were 142, 368 and 184 μm, respectively Cleal et al. 2007). Results The experiental data coe fro a set of experients reported previously Cleal et al. 2007). The experiental data in Fig. 2A were included in the previous paper in suary for. The data in Fig. 2B were not included in the previous work. All other data presented here represent novel output of the odel based on raw data fro these experients. Serine release The coparison between the odel predictions and experiental data is shown in Fig. 2, for a representative experient. Overall, the odel was observed to provide an excellent representation of both fetal and aternal serine levels, except for the initial phase between initiating substrate perfusion and reaching the initial diffusive equilibriu, in which the odel displayed a considerable overprediction. As in the experient, the adinistration of alanine boluses in the odel induced an iediate serine release into the fetal circulation. Interestingly, the odel also predicted the appearance of sall secondary aternal peaks. These sall peaks also appeared to be present in a nuber of the experients; however, it is iportant to note that their height was not significantly above the easureent noise level. Paraeter estiation The individual variability in estiated paraeters between the fits of the different experients is shown in Fig. 3A. The paraeter P for paracellular diffusion was estiated to be 1.8 ± s 1, Vexc ax for ASCT1/2 in the BM was 2.2 ± ol 2 s 1 and Vacc ax for syste A in the MVM was 2.4 ± ol 2 s 1. In general, the paracellular diffusion displayed the least variation, followed by the estiated transporter paraeters for ASCT1/2 and syste A, although in all cases the paraeters for the different experients were found to be well within the sae order of agnitude. Fro the overview of the fit quality for the different experients, it can be observed that the odel was able to closely eet the fitting criteria with respect to peak heights and fetal and aternal baseline values Fig. 3B). Peak area was not a fitting criterion; however, it was found that the peak area predicted by the odel atched reasonably well with the experiental data, although the odel tended to overpredict the area of the first peak ratio odel/experient 1.4 ± 0.3), and less so for the second peak ratio 1.2 ± 0.1). Model sensitivity Figure 4 shows a selection of the effects on the fit quality as a result of varying the estiated paraeters for each of the experients. As expected, the paracellular diffusion P directly regulated the fetal baseline value Fig. 4B). Low diffusion P did not affect fetal peak height. Note that the ai here was to give a clear overview of sensitivity, so these values do not necessarily represent the physiological range, since the increase in fetal peak height for very high diffusion will not occur in practice because the predicted baseline was already well outside the experiental results. The exchange rate for the ASCT1/2 transporter in the BM directly controlled peak height, as expected, but had only a liited effect on baseline values Fig. 4B and E). Perhaps surprisingly, high syste A activity in the MVM was predicted to affect the height of the serine release peaks in the experient. This is related to the increased accuulation of radiolabelled serine tracer in the syncytiotrophoblast. High syste A activity in the MVM also affected fetal baselines by lowering aternal concentrations and thus decreasing paracellular diffusion. Inaddition,anoverviewoftheodelsensitivityisgiven in Table 2, relative to the fitted reference configuration. With respect to fetal serine exchange, it can be seen that the Michaelis Menten constant for ASCT1/2 did affect exchange within the experiental concentration range. Surprisingly, it can be observed that LAT2 on the aternal side in the MVM also controlled fetal peak height. This is due to an increased initial exchange of radiolabelled serine, leading to higher levels of tracer in the syncytiotrophoblast. A high LAT2 V ax also sooths the jup in fetal baseline serine after the start of the aternal aino acid infusion by initially lowering aternal tracer levels and thus paracellular diffusion Fig. 2). The iportance of tracer accuulation and concentration is also apparent fro the effects of syncytiotrophoblast volue and its initial concentrations. Fetal volue is also an iportant paraeter; higher fetal volue fractions than the one used based on capillary volue alone led to lower and broader peaks; however, saller fetal volues did not affect serine exchange. Physiological aino acid levels For the siulations with a cobined input of serine, alanine and glycine, both the aternal and the fetal output concentrations were slightly lower <10%) than their respective input for each aino acid results not shown). Thus, no net transport across the placenta was observed

8 836 B. G. Sengers and others Exp Physiol 95.7 pp for any aino acid, and only a continued accuulation in the syncytiotrophoblast occurred. Surprisingly, looking at exchange only, by switching off accuulative transporters and paracellular diffusion, it was observed that for the in vivo concentrations used, the syste already started out approxiately in equilibriu. Discussion This study presents a novel coputational odelling fraework for aino acid transfer across the placenta. The odel successfully represented coplex transport interactions between ultiple transporters and substrates, specifically with respect to serine exchange in response to fetal alanine adinistration. Significantly, the odel accounted for different transport echaniss in both the fetal- and the aternal-facing ebranes of the syncytiotrophoblast as opposed to generalized transport through a single layer as in ost previous placental solute transfer odels for nutrients/oxygen. Incorporating both exchangers and accuulative transporters in the odel clearly deonstrated how these different echaniss can work together as an integrated syste. It also allowed assessent of their relative iportance in defined conditions. The results confired that the induced serine exchange was ost sensitive to BM transporter Figure 3. Paraeter estiation A, values of the estiated paraeters for the five different experients. The variation between individual placentae was saller than a factor of two for paracellular diffusion and ASCT1/2 BM, but slightly higher for syste A MVM. B, overview of the fit quality for peak 1 height and area, as well as fetal and aternal baselines. For fetal peak 2, the fit quality of peak height was siilar, while peak area atched ore closely to the experient data not shown).

9 Exp Physiol 95.7 pp Modelling placental aino acid transfer 837 characteristics, but also revealed a wide range of secondary, less intuitive effects related to aino acid accuulation in the syncytiotrophoblast. While this work only addressed a relatively siple three aino acid syste, the approach can be readily extended to incorporate additional experiental paraeters and will ultiately allow analysis of ore coplex physiological siulations. Quantitative estiation of physiological transport capacities One of the key advantages of the coputational odel was that it allowed quantitative estiates of physiological transport capacities V ax ) by fitting the experiental results. This provides iportant inforation that has not previously been available for the intact tissue. The ain result found was that the exchange capacity in the BM on the fetal side ASCT1/2) was an order of agnitude lower than transport across the MVM on the aternal side Fig. 3A). This would iply that transport across the BM will be rate liiting. However, on the fetal side only short alanine pulses were used in the experient. While this was a strong indication that the response tie of the syste was rapid, certain parts of the syste ay only be fully accessible on a longer tie scale, due to possible diffusive lag ties in the fetal stroa or endothelial layer. Thus, to deterine whether the syste is used up to its full capacity it will also be necessary to investigate sustained exchange with a constant fetal input and copare this to odel predictions. Iproved experiental interpretation The odel also allowed the evaluation of the effects of tracer accuulation in conducting the experient. For exaple, the odel showed how the ratio between labelled and unlabelled serine will initially vary due to the presence of unlabelled serine in the syncytiotrophoblast at the start of the experient. However, the odel predicts that the iplications for the interpretation of the experiental results are likely to be liited, since onitoring labelled Figure 4. Paraeter variation Effect on fit quality for each of the siulated experients different sybols indicate different experients). Height of fetal peak 1 and fetal baseline are shown as a function of the variation in paracellular diffusion P A and D), Vexc ax for ASCT1/2 in the BM B and E) andvacc ax for syste A in the MVM C and F). The vertical line indicates the reference paraeter value i.e. variation factor = 1). The horizontal line indicates a perfect fit ratio odel/experient = 1).

10 838 B. G. Sengers and others Exp Physiol 95.7 pp Table 2. Paraeter variation: overview of odel sensitivity Height of Height of Area of Area of Fetal Maternal peak 1 % peak 2 % peak 1 % peak 2 % baseline baseline change) 0.1, change) 0.1, change) 0.1, change) 0.1, % change) % change) Paraeter , , 10 P, paracellular diffusion 4, 32 5, 43 7, 23 9, 24 88, 322 4, 15 Vexc ax, ASCT1/2, BM 83, , , , 617 2, 11 0, 0 Vexc ax, LAT2, MVM 33, 76 29, 54 34, 73 29, 44 2, 2 4, 0 Vacc ax,systea,mvm 13, 31 6, 11 12, 27 6, 9 12, 57 13, 58 Vacc ax,systea,bm 1, 8 1, 5 0, 7 1, 8 3, 20 0, 1 K exc, ASCT1/2, BM 43, 67 22, , 73 70, 68 7, 2 0, 0 K exc, LAT2, MVM 30, 33 21, 29 31, 34 20, 29 0, 2 1, 4 K acc, syste A, MVM 14, 12 8, 6 14, 11 8, 5 18, 12 18, 12 K acc, syste A, BM 18, 2 12, 1 20, 0 14, 0 14, 3 0, 0 v, aternal volue 6, 10 7, 8 0, 7 0, 8 0, 0 0, 0 v s, syncytiotrophoblast volue 81, 74 32, 70 74, 74 31, 69 6, 13 4, 9 v f, fetal volue 8, 51 5, 45 6, 76 6, 83 0, 2 0, 2 c i s0, initial concentrations 61, 73 25, 68 56, 73 24, 68 6, 13 4, 10 The table shows relative changes with respect to fitted reference values when paraeters were either decreased or increased by a factor 10. An average was taken over siulations for all five experients. Changes greater than 50% are indicated in bold. For definition of paraeters, see ain text. serine resulted only in an up to 8% underestiation of total fetal serine output. In the experient, the second bolus was twice the concentration of the first bolus to assess the effect of Michaelis Menten kinetics in general. Indeed, the easured height of the second peak was higher than that of the first. However, depending on the experient, the odel predicts that the second peak can be up to 35% higher, even when the sae bolus concentration is injected. This is due to the steady accuulation of serine in the syncytiotrophoblast, which changes the relative coposition and ratio between serine and alanine over tie. However, this has to be explored in greater detail in future studies. The iportance of relative aino acid concentrations Since only accuulative transporters and exchangers transport serine, glycine and alanine Table 1), the odel would predict a continuous increase in the total aino acid concentration in the syncytiotrophoblast. However, in the physiological situation this build-up would be prevented by exchange for fetal and aternal aino acids not present in the experiental set-up, cobined with efflux of these aino acids via basal ebrane efflux transporters Cleal & Lewis, 2008). In addition, concentrations can be affected by aino acid etabolis in the placenta Cleal & Lewis, 2008). Interestingly, the reported in vivo aternal, placental and fetal aino acid concentrations were approxiately at the equilibriu values that would be arrived at due to the action of exchangers. The existence of this equilibriu in vivo suggests that the aino acid exchangers have an iportant role in deterining aino acid concentrations in these three copartents. This equilibriu resulted fro the approxiately equal ratios between serine and alanine in each of the different copartents serine/alanine: aternal 0.35, syncytiotrophoblast 0.36 and fetal 0.39), and was thus not affected by the ajor differences in absolute values and gradients across the ebrane. For exaple, if 35% serine goes in and 35% goes out in exchange, then no net transport occurs. The iportance of differences in intracopartental aino acid ratios rather than absolute gradients in the case of ultiple aino acids is further illustrated by observations that aternally infusing a ix of aino acids can in fact decrease the fetal uptake of specific aino acids, despite the increased aternal concentration, as a result of copetitive inhibition Jozwik et al. 2004). This underlines the iportance of the quantitative interactions between aino acids in understanding placental function as an integrated syste and has obvious iplications for clinical aino acid infusion strategies Paolini et al. 2003). Indirect exchange Interestingly, the odel predicted the occurrence of sall aternal serine peaks coinciding with the fetal serine release peaks Fig. 2). Maternal serine is always higher than fetal in the experient, so this is not siply a case of the fetal peak diffusing back towards the aternal side. Instead, this is the result of an indirect exchange echanis, in which the fetal alanine bolus rapidly diffuses towards the aternal side and there causes serine exchange via LAT2. The odel predicted that these secondary peaks on the aternal side will always be sall.

11 Exp Physiol 95.7 pp Modelling placental aino acid transfer 839 Indeed, there is soe indication that sall peaks of siilar agnitude did occur in a nuber of the experients; however, these results need to be confired by ore precise easureents. Transporter odelling The ain focus of the present odelling fraework was on the interactions between the different transporters in both MVM and BM and how these can work together as an integrated syste, governing placental transport of ultiple aino acids. It has to be ephasized, however, that the odel necessarily incorporated highly siplified relationships for the function of the aino acid exchangers, rather than the detailed biocheistry of the specific transporters, and that the olecular echaniss of ebrane transport are highly coplex in theselves. For exaple, intracellular and extracellular K for a transporter can be different, as has been deonstrated by Meier et al. 2002), who overexpressed specific aino acid exchangers in Xenopus oocytes, allowing detailed characterization of the transporter function. Different internal and external substrate affinities K )canbe explicitly inserted in the exchanger odel in eqn 5). However, at this point there are not sufficient data regarding both internal and external K values for these transporters and therefore the sae values were adopted. Notably, while the odel specifically addressed copetition between aino acids, an equal affinity for different aino acids was assued. This proved to be sufficient to represent the experiental data; however, these siplifying assuptions need to be revisited as the odel is expanded to include a wider range of aino acids. For exaple, copetitive inhibition by aino acids with different transporter affinity has been deonstrated in a ore phenoenological ultiple regression analysis of the uptake of aino acid ixtures using siilar Michaelis Menten relationships Paolini et al. 2003; Jozwik et al. 2004). Mebrane potential ayalsobeaniportantissuethatneedstobetaken into account in a ore coplex odel, especially for charged aino acids. Thus, as experiental validation data becoe available, increasingly coplex and realistic transporter relationships need to be incorporated into the odelling fraework. Placental structure and blood flow Initially, a highly siplified three copartent odel was adopted. The ost iportant assuption was that each copartent was considered to be well ixed. Clearly, this is not necessarily the case and, for exaple, the discrepancy between odel and experient in the initial phase after the start of the aternal aino acid infusion Fig. 2) is likely to be attributable to inadequate ixing in the aternal intervillous space. Furtherore, the fetal capillary network is clearly not a single well-ixed volue. Therefore, in addition to the three copartent odel, also a parallel capillary odel was developed, based on siple plug flow through a set of tubes of equal length. The predictions of both odelling approaches differed with respect to the peak delay and peak width for large fetal volues. However, for the sall fetal volues considered in this study both odels gave alost identical results. The three copartent odel was therefore adopted for coputational efficiency, since our ain focus was on aino acid exchange interactions. However, in what conditions flow and geoetry affect exchange need to be investigated further and it ay be necessary to integrate our detailed transporter odel with ore realistic fluid flow odels Franke et al. 2003; Alastruey et al. 2009; Chernyavsky et al. 2010). While this work focused on the huan placenta, it is expected that the general odelling fraework could be equally applied to different species, subject to separate validation, considering differences in substrate specificities, transport kinetics and the significant variation in placental structure between species Sibley, 2009). Conclusion The coplexity of placental aino acid transport eans that it is difficult to deterine intuitively how all the coponents work together as a syste. Modelling can provide a valuable insight into how placental aino acid transport works as a syste, identify the rate-liiting steps in the process, and deterine the effects of physiological changes in placental aino acid concentrations, transporter levels, blood flow or placental structure. Thus, in cobination with experients, an integrated odel for aino acid transport in the placenta has the potential to elucidate the highly coplex interactions between ultiple aino acids in a quantitative anner and to provide insight into the key deterinants of fetal growth. Hopefully, this will ultiately lead to targeted interventions and new strategies for ipaired fetal growth. References Alastruey J, Sherwin SJ, Parker KH & Rubens DD 2009). Placental transfusion insult in the predisposition for SIDS: a atheatical study. Early Hu Dev 85, Brand AP, Greenwood SL, Glazier JD, Bennett EJ, Godfrey KM, Sibley CP & Hanson MA 2010). Coparison of L-serine uptake by huan placental icrovillous ebrane vesicles and placental villous fragents. Placenta 31,

12 840 B. G. Sengers and others Exp Physiol 95.7 pp Brownbill P, Mahendran D, Owen D, Swanson P, Thornburg KL, Nelson DM & Sibley CP 2000). Denudations as paracellular routes for alphafetoprotein and creatinine across the huan syncytiotrophoblast. A J Physiol Regul Integr Cop Physiol 278, R677 R683. Castellucci M & Kaufann P 2006). Basic structure of the villous trees. In Pathology of the Huan Placenta,ed. Benirschke K, Kaufann P & Baergen R, pp Springer, New York. Chernyavsky IL, Jensen OE & Leach L 2010). A atheatical odel of intervillous blood flow in the huan placentone. Placenta 31, Cleal JK, Brownbill P, Godfrey KM, Jackson JM, Jackson AA, Sibley CP, Hanson MA & Lewis RM 2007). Modification of fetal plasa aino acid coposition by placental aino acid exchangers in vitro. JPhysiol582, Cleal JK & Lewis RM 2008). The echaniss and regulation of placental aino acid transport to the huan foetus. JNeuroendocrinol20, Costa A, Costantino ML & Fuero R 1992). Oxygen exchange echaniss in the huan placenta: atheatical odelling and siulation. J Bioed Eng 14, Erian FF, Corrsin S & Davis SH 1977). Maternal, placental blood flow: a odel with velocity-dependent pereability. J Bioech 10, Franke VE, Parker KH, Wee LY, Fisk NM & Sherwin SJ 2003). Tie doain coputational odelling of 1D arterial networks in onochorionic placentas. ESAIM Math Model Nuer Anal 37, Grooe LJ 1991). A theoretical analysis of the effect of placental etabolis on fetal oxygenation under conditions of liited oxygen availability. Biosystes 26, Guilbeau EJ, Reneau DD & Knisely MH 1973). A detailed quantitative analysis of O 2 transport in the huan placenta during steady- and unsteady-state conditions. In Cheical Engineering in Medicine, ed. Reneau DD, pp Aerican Cheical Society, Washington. Jansson T, Ylven K, Wennergren M & Powell TL 2002). Glucose transport and syste A activity in syncytiotrophoblast icrovillous and basal plasa ebranes in intrauterine growth restriction. Placenta 23, Johnson LW & Sith CH 1988). Neutral aino acid transport systes of icrovillous ebrane of huan placenta. A J Physiol Cell Physiol 254, C773 C780. Jozwik M, Teng C, Wilkening RB, Meschia G & Battaglia FC 2004). Reciprocal inhibition of ubilical uptake within groups of aino acids. A J Physiol Endocrinol Metab 286, E376 E383. Kekuda R, Prasad PD, Fei YJ, Torres-Zaorano V, Sinha S, Yang-Feng TL, Leibach FH & Ganapathy V 1996). Cloning of the sodiu-dependent, broad-scope, neutral aino acid transporter B o fro a huan placental choriocarcinoa cell line. J Biol Che 271, Kudo Y & Boyd CA 2001). Characterisation of L-tryptophan transporters in huan placenta: a coparison of brush border and basal ebrane vesicles. JPhysiol531, Lewis RM, Glazier J, Greenwood SL, Bennett EJ, Godfrey KM, Jackson AA, Sibley CP, Caeron IT & Hanson MA 2007). L-Serine uptake by huan placental icrovillous ebrane vesicles. Placenta 28, Mackenzie B, Schafer MK, Erickson JD, Hediger MA, Weihe E & Varoqui H 2003). Functional properties and cellular distribution of the syste A glutaine transporter SNAT1 support specialized roles in central neurons. J Biol Che 278, Mayhew TM 2009). A stereological perspective on placental orphology in noral and coplicated pregnancies. J Anat 215, Meier C, Ristic Z, Klauser S & Verrey F 2002). Activation of syste L heterodieric aino acid exchangers by intracellular substrates. EMBO J 21, Paolini CL, Marconi AM, Ronzoni S, Di Noio M, Fennessey PV, Pardi G & Battaglia FC 2001). Placental transport of leucine, phenylalanine, glycine, and proline in intrauterine growth-restricted pregnancies. J Clin Endocrinol Metab 86, Paolini CL, Teng C, Jozwik M, Meschia G, Wilkening RB & Battaglia FC 2003). Ubilical threonine uptake during aternal threonine infusion in sheep. Placenta 24, Philipps AF, Holzan IR, Teng C & Battaglia FC 1978). Tissue concentrations of free aino acids in ter huan placentas. A J Obstet Gynecol 131, Pinilla J, Barber A & Lostao MP 2001). Active transport of alanine by the neutral aino-acid exchanger ASCT1. Can J Physiol Pharacol 79, Pinilla-Tenas J, Barber A & Lostao MP 2003). Transport of proline and hydroxyproline by the neutral aino-acid exchanger ASCT1. J Mebr Biol 195, Schid-Schönbein H 1988). Conceptional proposition for a specific icrocirculatory proble: aternal blood flow in heochorial ultivillous placentae as percolation of a porous ediu. Trophoblast Res 3, Schröder H 1982). Fluid shift across the placenta: III. Application of a coputer odel of passive placental transfer. Placenta 3, Sebire NJ, Jain V & Talbert DG 2004). Spiral artery associated restricted growth SPAARG): a coputer odel of pathophysiology resulting fro low intervillous pressure having fetal prograing iplications. Pathophysiology 11, Segawa H, Fukasawa Y, Miyaoto K, Takeda E, Endou H & Kanai Y 1999). Identification and functional characterization of a Na + -independent neutral aino acid transporter with broad substrate selectivity. J Biol Che 274, Sibley CP 2009). Understanding placental nutrient transfer why bother? New bioarkers of fetal growth. JPhysiol587, Van Den Wijngaard JP, Westerhof BE, Ross MG & van Geert MJ 2007). A atheatical odel of twin-twin transfusion syndroe with pulsatile arterial circulations. A J Physiol Regul Integr Cop Physiol 292, R1519 R1531. Wasa M, Wang HS & Okada A 2002). Characterization of L-glutaine transport by a huan neuroblastoa cell line. A J Physiol Cell Physiol 282, C1246 C1253. Wilbur WJ, Power GG & Longo LD 1978). Water exchange in the placenta: a atheatical odel. A J Physiol Regul Integr Cop Physiol 235, R181 R199.