Novel multimodal molecular imaging of Vitamin H (Biotin) transporter activity in the murine placenta

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Maternal-fetal biotin transport.
To assess maternal-fetal biotin transport, biotin-Fluorescein (0.5 mg in PBS, Sigma-Aldrich) was administered to pregnant B6 mice at E14.5 (n = 4, 12 embryos) via tail vein. Mice were euthanized 60 min post injection. Placentae and embryos were fixed and sectioned serially. Histological sectioning was done for only a few consecutive slices, located at the mid sagittal section of the placenta. Placentas were fixed in Carnoy mixture, embedded in paraffin, and sectioned serially at 4-μm thickness.
Gadolinium content was independently determined by inductively coupled plasma mass spectrometry (ICPMS). Samples were homogenized with three equivalents of deionized water, and 100 µl of homogenate were lyophilized. Dry samples were digested with 200 µl of concentrated nitric acid (70%) overnight and heated in a dry bath for one hour at 90 °C. Standard, 10-ml samples were prepared with deionized water and analyzed by ICPMS (ELAN-6000 instrument; Perkin Elmer, Norwalk, CT). Statistical analysis of ICPMS data consisted of calculating the mean ± standard error of the mean (SEM). Differences between measurements were compared with repeated measures of two-way ANOVA using GraphPad Prism version 5.00 for Windows (GraphPad Software, San Diego, CA, USA).
A group of mice (n = 10), were injected with b-BSA-GdDTPA using a bolus injection was via a tail vein catheter (Group A). A second competition group (n = 5) was injected with native biotin three minutes prior to administration of b-BSA-GdDTPA (group B). Dynamic T 1 -weighted 3D-GRE images were acquired at 20 time points post contrast injection for a total of 54 min.
During the course of these measurements, the concentration of the contrast agent changed continuously throughout all placental compartments. To assess contrast-agent perfusion kinetics, the mean signal intensity (SI) was recorded across the 20 time points and for each placenta. Due to the limited MRI frame rate (~ 3 min per scan), the concentration in each compartment was assumed to be stepwise constant for each individual scan. This resulted in a time-dependent signal, S (n) | n=1…20 , for each voxel in the placenta.
Placental regions of interest (ROIs) were marked using a semi-automated routine in Analyze Direct 11.0 (AnalyzeDirect Inc), initiated from manually planted seed points (Fig. 1a). ROIs were also drawn for the vena cava (maternal arterial input) and embryonal hearts. Three-dimensional data reconstruction was performed with AMIRA software (AMIRA, Mercury Computer Systems, Berlin, Germany) and Avizo software (Visualization Science Group, Burlington, MA) and movies displaying the DCE data were produced with Imaris Software (Bitplane AG, Zurich, Switzerland). www.nature.com/scientificreports/ Three-compartmental model of placental architecture. The placenta was modeled to consist of three microstructural sub-voxel compartments (Fig. 2): C1, large maternal blood pool, having a constant level of b-BSA-GdDTPA; C2, Spiral arteries perfusing the placenta; and C3, fetal trophoblast cells lining the labyrinth. In vivo DCE-MRI data cannot resolve these compartments, and were analyzed based on the assumption that each macroscopic voxel (size 150 × 150 × 625 µm 3 ) contains contributions from C2 and C3, with C1 being easily detected and excluded from the processing. Following the bolus injection into C1, the contrast material is transported into C2 and C3 until a steady state is reached. The constant concentration in C1 was estimated to be approximately 100 mM based on the amount of contrast material injected divided by blood volume. Perfusion and inter-compartmental exchange evolved according to the following pair of differential equations: (1)  www.nature.com/scientificreports/ where c 1 , c 2 , and c 3 are the concentrations within each compartment, ċ i (i = 1, 2) represent the derivatives of each compartment's concentration with respect to time, and k 12 and k 23 denote unidirectional inter-compartmental exchange rate constants. A detailed solution of these equations is given in the Appendix. The time dependent concentrations within each compartment were used to compute the relaxation rates R 1 (t) and R 2 (t) using typical relaxivity values 12 : These values were then set into the steady-state signal equation for gradient echo (GRE) DCE-MRI 12 yielding the time dependent signal arising from each voxel in the MRI images Here θ denotes the excitation flip angle, M 0 the proton density weighted by the receiver coil sensitivity profile, TR/TE the repetition/echo time, and T * 2 the local field inhomogeneity.
The effects of contrast agent aggregation. Beyond its direct effect as a T 1 -shortening agent, b-BSA-GdDTPA affected relaxation rates via the formation of aggregates (Fig. 3). These influence the MRI signal in a manner that does not follow the pattern associated with soluble Gadolinium (Eq. 5), but rather create strong microscopic distortions of the local magnetic field, which lead to significant changes in R 2 * and attenuate the signal up to two orders of magnitude higher than those caused by soluble gadolinium. Mathematically, this effect was incorporated into Eq. (5) by adding an aggregate attenuation term,R * 2,Agg , Figure 2. Placental three compartmental model. Placental internal structure is modeled as three main compartments. C1: the maternal arterial input; C2: the maternal intravascular compartment; and C3: the trophoblast cell compartment. k 12 represents the rate of contrast agent flow from C1 into to C2 in the placenta and k 23 represent the rate of contrast active uptake by the C3 compartment. Contrast material concentration within C1 was measured, and found to remain constant and equal to 104 µM ± 12.32 SD, N = 10. T1 and T 2 * relaxation effects are shown in each compartment. While T 1 relaxation is constant, the T 2 * effect at C2 as a result of aggregate formation, is mediated via biotin transporters of the trophoblast cells lining the maternal sinuses, and the T 2 * effect at C3 is mediated via active contrast-agent uptake by trophoblasts in the placental labyrinth. Later, retention in aggregate followed by recycling and dispersion is mediated via the C3 trophoblast cells in the labyrinth, which is concordant with the SI recovery phase in the MRI signal. www.nature.com/scientificreports/ Due to their large effect on the signal, aggregate formation and clearance were easily identified by analyzing the MRI time-series and marking the time points of signal reduction (aggregate formation) and recovery (aggregate clearance) at each voxel. The output of this procedure were two parametric maps, T formation and T clearance, representing the transition time-points between the three aggregation phases (signal elevation, attenuation, and recovery).

2,Agg
Generation of quantitative MRI parametric maps. The time-dependent signal, S (n) | n=1…20 , from each voxel in the placenta, was fitted to the theoretical model in Eq. (6). Six unknown parameters exist in the model: the unidirectional exchange rate constants k 12 and k 23 , the aggregate-induced relaxation rates ( R * 2,Agg ) during the elevation, reduction, and recovery phases, and V 23, the volumetric fraction between the maternal (C2) and fetal (C3) compartments in each voxel. The remaining variables were extracted from the experiment, and included the signal intensity, repetition time, TR, echo time, TE, and flip angle, θ.   www.nature.com/scientificreports/ To determine the unknown parameters in Eq. (6), we first simulated the signal produced by our MRI protocol on a standard desktop PC. Simulations were implemented using MATLAB (The Mathworks Inc., Natic, MA) and were repeated for a range of physiological parameter values, producing a dictionary of ~ 170,000 different signal time-courses, each corresponding to a unique six-fold set of parameter values [k 12 , k 23 , R * 2,Agg @SI Elevation , To determine the values of these parameter at each voxel, we matched the experimental time-curve at each voxel, to the entire set of dictionary entries using exhaustive search. The optimal value was then chosen based on a similarity criterion, defined as the minimal L2-norm between the experimental and simulated curves. The end-product of this process was a set of six parametric maps, describing the exchange rates, k 12 and k 23 ; contrast-agent aggregation at elevation, reduction, and recovery; and volumetric fraction, V 23 , for each imaged slice and for each placenta. Placentae were histologically labeled for b-BSA-GdDTPA, with Avidin-FITC, and analyzed using Fiji image processing and analysis software 13,14 . Fiji procedures were developed and optimized to individually segment aggregates, trophoblast cells, and placentae. A Fiji macro was developed for quantifying aggregation of Avidin-FITC-labeled b-BSA-GdDTPA by segmenting the aggregated structures, excluding the nuclei. This macro segmented distinct aggregates using connected component analysis 15 and produced the total number of aggregates, their individual areas, and total aggregate area. All values were further normalized by the placenta area. Aggregates were sorted according to size (small < 50 µm, 50 µm < medium < 500 µm, or large > 500 µm) and calculated the number and total area covered by each size group.
To identify trophoblast cells, nuclei were segmented from the blue (DAPI) channel in several steps: (1) Nuclei were enhanced using a bandpass filter, which then were processed with automatic "RenyiEntropy" thresholding method 16 ; (2) Small holes in the nuclei were filled and neighboring nuclei were separated using a binary watershed method 17 ; (3) Aggregates in the GFP channel were masked by automatic thresholding with the "Max-Entropy" method 18 . Nuclei were excluded from this mask, which was also used for the segmentation of extracellular aggregates. Small aggregates (< 5 µ 2 ) were ignored. Segmentation of the whole placenta was achieved by combining the GFP and the blue channels into an 8-bit image, and applying a Gaussian blur filter 19 , together with automatic thresholding ["Mean" method], and closing holes using morphological dilation and erosion operations.
Statistical analysis of aggregate size and count. The relative aggregate area was calculated by dividing total aggregate area by placental area. Groups were compared by one-way ANOVA, followed by a Tukey post-hoc test. Aggregates were also separated into small, medium, and large size groups as defined above, and the same comparison was performed for each size group. The relative number of aggregates was calculated by dividing the number of aggregates by the placenta size. Groups were compared by one-way ANOVA, followed by a Tukey post-hoc test. Comparisons were also made for each size group, as was done for aggregate area.
Validating the role of biotin transporters using BSA-ROX experiments. To further confirm the involvement of biotin-transporters in the perfusion and aggregation mechanism fluorescent BSA labeled with rhodamine (BSA-ROX, 4 mg in 0.6 ml PBS, Rhenium, Israel) was administered to pregnant B6 mice at E14.5 (n = 4, 12 embryos) via tail vein 60 min prior to animal euthanizing as reported previously 20 . Placentae were fixed, sectioned, and analyzed serially. Histological sectioning was done for only a few consecutive slices, located at the mid sagittal section of the placenta. Placentas were fixed in Carnoy mixture, embedded in paraffin, and sectioned serially at 4-μm thickness.
Validation of biotin-transporter mediated kinetics using PET imaging. Biotin transporter-mediated kinetics were also validated using PET imaging. Competition experiments were conducted, similar to the MRI study design. In this case [ 18 F] Biotin tracer was injected to two groups of pregnant CD1 mice (E18-20): the main experimental (n = 37 fetuses and placentae), and a competition group (n = 39), which was pre-injected with a non-radiolabeled D-biotin in order to test the hypothesis that the accumulation of radiolabeled CA is mediated by biotin transporters. Dynamic PET data were acquired for 20 min, followed by a 5-min CT scan, and concluding with a 40-min dynamic PET scan. Immediately following the 2 nd PET acquisitions, mice were sacrificed for biodistribution. Organs and tissues of interest, including each fetus, associated placenta and uterus, were harvested, weighed and the radioactivity was measured using a gamma counter. The uptake, %ID/g, of [ 18 F]Biotin in the fetuses and placentae in each group were compared by one-way ANOVA followed by a Tukey's post-hoc test.

Results
Biotin-fluorescein histology reveals biotin transport from the mother to fetus. Fluorescent images of biotin within the placentae and adjacent fetuses are shown in Fig. 4, confirming the transport of free biotin from the mother to the fetuses. Following injection of contrast, Biotin-Fluorescein accumulated within red blood cell (RBCs) in the blood spaces of the maternal placenta (MBS) and in the RBCs of the embryonic blood spaces (EBS) in the labyrinth (Fig. 4a-d). In the Fetus, Biotin-Fluorescein accumulated in the fetal heart, liver and thymus (Fig. 4e-h). , and a signal recovery stage (30-60 min). As validated by histology, signal attenuation was caused by aggregation of the CA. In the competition experiment (where excess native biotin was injected prior to administration of b-BSA-GdDTPA), lower initial elevation was observed, signal reduction was eliminated, and the period of signal plateau was extended (Fig. 1b,d).
Signal changes were simultaneous within all the placentae of a litter, and exhibited consistent spatiotemporal directionality: signal attenuation started from the decidua zone, propagated toward the spongiotrophoblast  www.nature.com/scientificreports/ junctional zone (Sp) and ended at the labyrinth zone, without crossing to the fetus due to the contrast agent large size (Fig. 1c). Signal recovery propagated in the opposite direction, i.e., from the labyrinth zone to the decidua, eventually leading to full recovery of placental signal. Signal in the maternal blood vessels (MBV) remained constantly high throughout the three signal phases (Fig. 1b). Additional videos and 3D rendering of the placenta perfusion, with and without biotin administration, are available in the supplementary materials (Fig. S1).

Histological validation of b-BSA-GdDTPA aggregation and dispersion patterns. Histological
analysis of placentae at each kinetic stage revealed aggregates forming in the maternal sinuses and labyrinth, as well as around and within the trophoblast cell layer during the signal elevation stage, right after injection of CA (Fig. 3a,d,g). Aggregate number increased during the signal reduction phase (p < 0.001, Fig. 3b,e,g), and then dispersed during the recovery phase (p < 0.01, Fig. 3c,f,g). Aggregate size increased from elevation to reduction phases (p < 0.01), with only minor changes observed during the subsequent recovery phase (p > 0.05, Fig. 3h).
The total area and perimeter of aggregates were congruent with the signal elevation-attenuation-recovery pattern (p < 0.001, Fig. S2). Analysis of aggregate distribution revealed maximal area coverage during the SI reduction phase (6.72%) compared with the elevation (1.73%) and recovery (2.1%) phases (p < 0.01, Fig. S2a). This suggests a change in aggregate morphology between the three phases. Further analysis of aggregates size-distribution and internal morphology (area and perimeter), revealed three size groups: ≤ 50 μm, 50…500 μm, and ≥ 500 μm, where the majority of aggregates during all phases was smaller than 50 µm (p < 0.001, Fig. S2c). Figure 3i shows the total placental Gd content estimated using ICPMS analysis, demonstrating a gradual accumulation of Gd in the placenta throughout 60 min following administration of b-BSA-GdDTPA. Placental gadolinium content did not vary significantly between the signal elevation and reduction phases, while there was a subsequent × 3.1-fold increase in Gd content during recovery phase (p < 0.01). Importantly, Gd content in the fetuses remained undetectable 60 min following contrast administration (p < 0.001).

Biotin competition experiment: histological validation of biotin-transporter-mediated kinetics. Biotin competition experiments consisted of injection of excess native biotin prior to injection of b-BSA-
GdDTPA. Fluorescent images demonstrate excessive spherical aggregation that did not disperse after 60 min ( Fig. 5d-f). The majority of these aggregates were of native biotin, while co-labeling for albumin demonstrated little overlap between biotin and b-BSA-GdDTPA, suggesting the inhibition of b-BSA-GdDTPA transport and aggregation due to the saturation of the biotin transporters by excess native biotin (Fig. 5f). On the other hand, stained tissue harvested from the mice injected with only b-BSA-GdDTPA demonstrated almost complete overlap of biotin and albumin staining, lining the perimeter of the maternal sinuses in the labyrinth, ruling out the dissociation of biotin from b-BSA-GdDTPA (Fig. 5a-c).
Modeling biotin kinetics using a mathematical three-compartment model. Figure 6 presents parametric maps for a representative placenta, calculated based on the three-compartment model (Methods "Three-compartmental model of placental architecture" section). The model consists of C1: maternal arterial input, C2: maternal intravascular compartment, and C3: the layer of trophoblast cells (see Fig. 2). Fitting the experimental data to the model produced six parametric maps with the following average values (collected across all mice): inter-compartmental unidirectional exchange rate constants k 12 = 0.045 ± 0.034 s −1 , and k 23 = 0.059 ± 0.035 s −1 ; three relaxation time constants linked to contrast-agent aggregates during the three signal phases: T * 2,Elevation = 63.3 ± 39.7 ms, T * 2,Reduction = 2.7 ± 1.6 ms, and T * 2,Recovery = 13.6 ± 10.0 ms. The last map shows the average volume fraction V 23 between the maternal blood pool C2, and trophoblast compartment C3. A V 23 value of 0.75 ± 0.25 was produced by the model, signifying that an average of 75% of the pixels belonged to C2 and 25% to C3 (Fig. 6g). A histogram of V 23 values is displayed in Fig. 6h. Representative fitting of simulated to experimental signal curves are illustrated in supplementary Fig. S3.

Validating the role of biotin transporters using BSA-ROX experiments. No aggregation was
observed in the placentas after injection of only BSA, unlabeled by biotin. This suggests that the aggregation of contrast-agent is indeed mediated by a cellular biotin-transporter mechanism (see Fig. S5). Figure 7a shows the structure of the biotin derivative studied (Fig. S6) as well as the relative uptake in the fetuses and placentae from three dams under non-blocking and three dams under blocking conditions. Fetuses from each litter were grouped together producing an average uptake in the non-blocking fetuses (n = 39) and placentae of 1.3 ± 0.2%ID/g and 2.8 ± 0.8%ID/g, respectively. Uptake of the tracer under blocking conditions (whereupon 1 mg of non-radiolabeled D-biotin was co-injected with the tracer) averaged at 0.47 ± 0.08%ID/g and 0.7 ± 0.2%ID/g in the fetuses and placentae (n = 37/tissue of interest). The difference in uptake between each set of organs was statistically significant. www.nature.com/scientificreports/

Discussion
Biotin transporter-mediated uptake and retention of biotinylated contrast agent. This study introduces MRI-based method for in vivo monitoring of biotin transporter kinetics in the murine placenta. We previously reported that administration of b-BSA-GdDTPA resulted in its active uptake by trophoblast cells in the labyrinth and by TGC cells, although the mechanism underlying this uptake remained unclear 21,22 . This study shows that biotin-BSA-GdDTPA uptake is mediated by biotin transporters residing on the trophoblast cells. Following initial MRI signal elevation due to perfusion of the biotinylated CA to the maternal placental blood pool, signal attenuation occurred due to aggregation of the contrast-agent in the maternal blood sinuses, the labyrinth, and their interface with the trophoblast cells, but not in the maternal spiral arteries. Later, MRI signal recovered, as aggregates underwent conformational change and recycling, indicative of an intracellular cell-mediated recycling mechanism. Our results suggest that the formation of aggregates is one of the biological mechanisms, used to regulate the transport of biotin to the fetus. The trophoblast cells use this mechanism to control retention and clearance of biotin, thereby possibly protecting the fetus from undesired fluctuations in nutrient transport and maintaining steady delivery of biotin.
To confirm the involvement of biotin in this recycling mechanism, we performed several validation experiments. First, no aggregation was observed when equal concentration of fluorescent albumin (BSA-ROX) was The specific contrast agent design used in this study affected trans-placental kinetics mainly due to the conjugation of biotin with the large Albumin molecule. This design enabled to isolate the activity of the transporter on the trophoblast surface while preventing its subsequent transfer into the fetal blood stream. The addition of the Gadolinium agent had a low effect on the dynamics, as it does not significantly increase the complex size. www.nature.com/scientificreports/ Complementing this picture were the fluorescence experiments, showing that low molecular weight biotin-only conjugates did cross into the fetal bloodstream utilizing the same transporter.
Twofold T * 2 effect: soluble gadolinium and aggregates of contrast agent. Contrast-agent aggregates formed when more than 10 mg/kg of b-BSA-GdDTPA was injected (supplementary Fig. S4). Gd can contribute to changes in T * 2 via two different mechanisms. The first is field heterogeneity around the soluble gadolinium chelate, operating at a molecular (nanometer) length scale. This effect is governed by diffusion of water molecules around the Gd complex, which is being randomly "sampled", thereby shortening T * 2 and increasing signal attenuation. The second mechanism is biotin-transporter-mediated formation of CA aggregates, operating at a cellular (micrometer) length scale. The mechanism was denoted as T * 2,Agg , and was up to two orders of magnitude stronger vis-à-vis soluble CA. Due to this sizable effect, it was the CA aggregates which dominated the MRI signal drop and recovery, easily identified on the DCE-MRI time-series. The spatial distribution www.nature.com/scientificreports/ of T * 2,Agg values reflected two distinct populations, attributed to two functional compartments (C2 and C3). Globally, aggregation-related signal drop exhibited spatial directionality starting at the decidua and the distal labyrinth, and propagating towards the labyrinth. Later, aggregate dispersion and signal recovery propagated back from the labyrinth toward the peripheral labyrinth and venous backflow through the junctional zone and decidua. These patterns correlated well with histology, showing a clear conformational change between signal drop and recovery stages, and supporting the dominant aggregate-mediated T * 2 effect in the maternal compartment, and the minor T * 2 effect within the intracellular trophoblast cells.
Three compartment model. MRI-based analysis of placenta perfusion is used frequently in animal studies and may have clinical utility in predicting pregnancy outcome 15 . While most studies report averaged perfusion values across the entire placenta, recent works suggest that perfusion differs significantly across different regions of the placenta 6,15 . Another factor, which confounds the dynamics of contrast enhancement and should be considered, are specific molecular recognition and transport. Specifically, this study demonstrated the importance of accounting for both placental perfusion and transporter mediated uptake.
The three-compartment model presented herein includes a maternal arterial input (C1), and two placental compartments: an inert maternal, intravascular compartment (C2), and a trophoblast-cell, intracellular compartment in which biotin is actively transported, accumulated and processed (C3). The three-compartment analysis of the MRI signal was based on the histologically validated premise that each voxel in the macroscopic MRI image, is composed of a heterogeneous mixture of compartments C2 and C3, whereas C1 can be easily identified and segmented as a spatially separate compartment. This architecture poses a considerable challenge for in vivo investigations, constraining most studies to the use of ex vivo methods, such as histology and corrosion casts 3 . Here, we incorporated the intricate placental architecture into a comprehensive spatiotemporal model of DCE-MRI signal. Contrast enhancement was excluded from the fetus by using a high molecular-weight b-BSA-GdDTPA that does not cross the placental barrier. The analysis of placental perfusion and biotin transport was thus not confounded by transfer of b-BSA-GdDTPA to the fetal circulation.
The significant correlation between the MRI model predictions and histology validates the functional separation of the labyrinth region of the placenta into two distinct compartments, C2 and C3, thus confirming the three-compartment hypothesis. The exact fractional ratio of compartments varied between placentae and mice, with an average of 75% C2 and 25% C3. Our k 12 and k 23 maps denote the inter-compartmental exchange rates, and reflect characteristic placental physiology, in which the fast exchange (C3) and slow exchange (C2) compartments are meshed in a heterogeneous manner. These findings provide new insights into placenta microstructure, molecular recognition, and transport machinery, adding to previous studies that focused on placental perfusion while assuming a clear spatial separation between the two compartments 6,15 . The quantitative model includes several parameters of interest: the exchange rates reflect whether biotin perfuses normally into and within the placenta; the extent of CA aggregation reflects the efficiency of the active transport mechanism; and the relative fractions of C2 and C3 manifest the placental cellular composition and whether the spiral arteries and trophoblast cells are normally distributed.
Calculated k 12 and k 23 values were consistent with previous reports on biotin transport 22,23 . Accordingly, slightly lower k 12 exchange rates are associated with the rapid flow of maternal blood into the C2 maternal compartment via large, relatively unobstructed arterial canals (C1 compartment). No aggregation was observed in these endothelial blood vessels, corresponding to the passive transport of fluids and contrast-agent into the C2 placental compartment. Trophoblast cells (C3 compartment) line the lumen of the maternal C2 compartment and mediate filtration of water and nutrients to the fetus. However, since there is no transport of b-BSA-GdDTPA to the embryo, the agent accumulates quickly and aggregated outside the trophoblast cells, consistent with the slightly higher k 23 exchange values. Lastly, b-BSA-GdDTPA aggregation and dispersion kinetics, suggest an active, biotindependent, recycling mechanism after biotin passively reaches the C2 compartment.
PET based validation of biotin distribution. 18 F uptake in the fetuses and placentae indicated that the uptake of the tracer could be inhibited with a co-injection of the non-radiolabeled D-biotin compound. On average, the summed SUV in each mouse was higher in the non-blocking mouse vs. that of the blocking mouse, a conclusion that aligned with the biodistribution data. PET experiments were thus in agreement with the MRI findings, further corroborating the conclusion that biotin transport is actively mediated by biotin transporters.
A more accurate quantitative comparison of kinetic parameters from two modalities is not feasible due to the fact that the physical mechanism behind the contrast agents' influence on the signal is different for MRI and for PET. Another, not less important factor, is that the high sensitivity of PET could be used for analysis of trace levels of biotin, while MRI requires much higher contrast media concentration (above physiological levels). However, while PET can detect only the amount of biotin in the tissue, MRI was sensitive to changes in the localization and intracellular environment of the contrast material, including aggregation and clearance.

Conclusions
This study reports two key advancements. The first is a demonstration that the transport of biotin to the fetus is actively mediated by placental biotin transporters resulting in biotin retention in intracellular aggregates. Our experiments revealed an active biotin uptake, retention, and clearance mechanism, as well as its spatiotemporal distribution in the placenta. The second advancement is the introduction of a new MRI-based tool that can accurately and reliably probe the structure and perfusion in murine placenta in vivo, as well as the dynamics of biotin transport and intracellular aggregation. The tool is based on a biophysical model of the placenta, which incorporates its microanatomy and physiology as well as the molecular dynamics of biotin transporter activity, into a comprehensive MRI signal model. The presented methodology can assist in monitoring biotin deficiency Scientific Reports | (2020) 10:20767 | https://doi.org/10.1038/s41598-020-77704-9 www.nature.com/scientificreports/ Boundary condition at time t = 0. At time t = 0 the CA concentrations in the placenta is zero. This can be expressed as Plugging in the expressions for c 2 and c 3 and rearranging terms, we obtain the solution to the constants A and B: Asymptotic behavior at time t = ∞. Before examining the asymptotic behavior of the concentrations, we draw attention to the sign of the constants β 1 and β 2 . Assuming, without loss of generality, that all exchange rates are nonnegative, it can be shown from (15) that both constants are always negative. It directly follows that the exponential terms in (16) will reduce to zero at later times, leading both c 2 and c 3 to be equal to c 1 indicating that the system eventually reaches a natural equilibrium across the three compartments C2, C3 and C1.
Translating concentrations to MR relaxation rates. The time-dependent concentrations within each compartment were used to calculate the corresponding changes in the R 1 and R 2 relaxation rates, using typical relaxivity (R 1 ) values 12 : Finally, these values were set into the steady-state signal equation for GRE MRI 12 yielding the time dependent signal arising from each voxel in the MRI images where θ denotes the excitation flip angle, M 0 the proton density weighted by the receiver coil sensitivity profile, and TR, TE the repetition and echo time, respectively.