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A mathematical model of the interaction between bovine blastocyst developmental stage and progesterone-stimulated uterine factors on differential embryonic development observed on Day 15 of gestation

Open ArchivePublished:November 02, 2017DOI:https://doi.org/10.3168/jds.2017-12845

      ABSTRACT

      A complex interaction between the developing bovine embryo and the growth potential of the uterine milieu it inhabits results in an embryo capable of developing past the maternal recognition stage and on to a successful pregnancy. Previously, we observed variation in the lengths of embryos recovered 8 d after bulk transfer of Day 7 in vitro-produced (IVP) blastocysts into the same uterus. Potential causes of the differential embryonic growth were examined and modeled using 2 rounds of bulk (n = 4–6) IVP transfers and recovery of these embryos 8 d later. Morphological and gene expression measurements of the embryos were determined and the progesterone concentration of the cows was measured throughout the reproductive cycle as a reflection of the status of the uterine environment. These data were used to develop and evaluate a model that describes the interaction between the uterine environment and the growth rate of the developing embryo. Expression of 6 trophectoderm genes (IFNT, TKDP1, PAG11, PTGS2, DKK1, and PDPN) was correlated with conceptus length. The model determined that if the embryo develops to blastocyst stage, the uterine environment, driven by progesterone, is a more important component than blastocyst size in the stimulation of embryonic growth rate to ensure adequate interferon tau (IFNT) for pregnancy recognition. We detected an effect of Day 7 progesterone on the expression of all 6 genes, embryonic disc size, and trophectoderm length on Day 15. We also found effects of embryo transfer size on trophectoderm length and expression of IFNT and PAG11 on Day 15. Lower energy balance over the period from transfer to recovery was associated with reduced embryo growth to Day 15, and this effect was independent of progesterone. Energy balance also affected expression of PDPN and TKDP1 on Day 15. We observed an effect of energy balance from transfer to recovery on embryo survival in cows with partial embryo losses, where embryo factors dominate embryo survival, with cows with greater energy balance having lower embryo losses. This effect was independent of energy balance 40 d before transfer and suggests that energy balance has direct, immediate effects on the embryo and maternal environment during this period. Furthermore, energy balance effects on embryo survival in cows with partial embryo losses were largely mediated by expression of TKDP1, PAG11, and PDPN. These results provide candidate signaling pathways for the effect of progesterone and energy balance on embryo growth and survival.

      Key words

      INTRODUCTION

      The developing ruminant conceptus is dependent on maternally derived factors including amino acids, cytokines, glucose, and growth factors present in the uterine luminal fluid for its growth and development beyond Day 7. These maternally derived factors are crucial for successful elongation of the blastocyst and have not yet been replicated successfully using in vitro production (IVP) techniques (
      • Brandão D.O.
      • Maddox-Hyttel P.
      • Løvendahl P.
      • Rumpf R.
      • Stringfellow D.
      • Callesen H.
      Post hatching development: A novel system for extended in vitro culture of bovine embryos.
      ;
      • Machado G.M.
      • Ferreira A.R.
      • Pivato I.B.
      • Fidelis A.
      • Spricigo J.F.
      • Paulini F.
      • Lucci C.M.
      • Franco M.M.
      • Dode M.A.
      Post-hatching development of in vitro bovine embryos from day 7 to 14 in vivo versus in vitro.
      ). The importance of uterine gland secretions into the histotroph has been demonstrated by the ablation of uterine gland development in the perinatal ewe, resulting in a maternal environment in which embryos fail to successfully elongate (
      • Gray C.A.
      • Burghardt R.C.
      • Johnson G.A.
      • Bazer F.W.
      • Spencer T.E.
      Evidence that absence of endometrial gland secretions in uterine gland knockout ewes compromises conceptus survival and elongation.
      ). The environment of the developing embryo is an essential regulator of interferon tau (IFNT) production, which overrides luteolytic mechanisms to allow the establishment and maintenance of pregnancy (
      • Spencer T.E.
      • Johnson G.A.
      • Bazer F.W.
      • Burghardt R.C.
      • Palmarini M.
      Pregnancy recognition and conceptus implantation in domestic ruminants: Roles of progesterone, interferons and endogenous retroviruses.
      ). Early in the estrous cycle, the secretion of uterine proteins into the lumen changes as the hormone profile changes. Progesterone is one of the main regulators of the genes expressed in the endometrium that are involved in the preparation of the uterus during early pregnancy (
      • Bazer F.W.
      • Roberts R.M.
      • Thatcher W.W.
      Actions of hormones on the uterus and effect on conceptus development.
      ;
      • Spencer T.E.
      • Johnson G.A.
      • Burghardt R.C.
      • Bazer F.W.
      Progesterone and placental hormone actions on the uterus: Insights from domestic animals.
      ) and this is reflected in the protein expressed in the uterine histotroph (
      • Ledgard A.M.
      • Berg M.C.
      • McMillan W.H.
      • Smolenski G.
      • Peterson A.J.
      Effect of asynchronous transfer on bovine embryonic development and relationship with early cycle uterine proteome profiles.
      ;
      • Forde N.
      • McGettigan P.A.
      • Mehta J.P.
      • O'Hara L.
      • Mamo S.
      • Bazer F.W.
      • Spencer T.E.
      • Lonergan P.
      Proteomic analysis of uterine fluid during the pre-implantation period of pregnancy in cattle.
      ). In beef heifers, elevation of progesterone concentrations on Days 5 and 7 after estrus results in an increase in the size of the conceptus at Day 16 (
      • Garrett J.E.
      • Geisert R.D.
      • Zavy M.T.
      • Morgan G.L.
      Evidence for maternal regulation of early conceptus growth and development in beef cattle.
      ;
      • Carter F.
      • Forde N.
      • Duffy P.
      • Wade M.
      • Fair T.
      • Crowe M.A.
      • Evans A.C.
      • Kenny D.A.
      • Roche J.F.
      • Lonergan P.
      Effect of increasing progesterone concentration from Day 3 of pregnancy on subsequent embryo survival and development in beef heifers.
      ) and it appears that the altered histotroph composition produces this effect rather than a direct effect of progesterone on the embryo (
      • Clemente M.
      • de La Fuente J.
      • Fair T.
      • Al Naib A.
      • Gutierrez-Adan A.
      • Roche J.F.
      • Rizos D.
      • Lonergan P.
      Progesterone and conceptus elongation in cattle: a direct effect on the embryo or an indirect effect via the endometrium?.
      ). Lactating cows have lower serum progesterone concentrations throughout the cycle compared with heifers (
      • Rizos D.
      • Carter F.
      • Besenfelder U.
      • Havlicek V.
      • Lonergan P.
      Contribution of the female reproductive tract to low fertility in postpartum lactating dairy cows.
      ), possibly because of the reported faster rate of metabolism of progesterone in lactating cows compared with nonlactating cows (
      • Sangsritavong S.
      • Combs D.K.
      • Sartori R.
      • Armentano L.E.
      • Wiltbank W.C.
      High feed intake increases liver blood flow and metabolism of progesterone and estradiol-17beta in dairy cattle.
      ). Embryonic mortality due to the uterine environment is as high as 13% for cows compared with 3% in heifers (
      • Berg D.K.
      • van Leeuwen J.
      • Beaumont S.
      • Berg M.
      • Pfeffer P.L.
      Embryo loss in cattle between Days 7 and 16 of pregnancy.
      ). Several factors other than progesterone may influence the difference in uterine luminal fluid composition, including nutrition and metabolic state of the animal (
      • Roche J.R.
      • Burke C.R.
      • Meier S.
      • Walker C.G.
      Nutrition x reproduction interaction in pasture-based systems: Is nutrition a factor in reproductive failure?.
      ). The combination of these factors will result in a downstream modulating effect on uterine protein levels present in the luminal fluid, which can be specific to individual animals (
      • Ledgard A.M.
      • Meier S.
      • Peterson A.J.
      Evaluation of the uterine environment early in pregnancy establishment to characterise cows with a potentially superior ability to support conceptus survival.
      ). One mode of action of the uterine influence may be on the metabolic growth rate of embryos, because it has been shown that Day 18 embryos recovered from heifers had more active biosynthetic pathways than those derived from lactating cows (
      • Valour D.
      • Degrelle S.A.
      • Ponter A.A.
      • Giraud-Delville C.
      • Campion E.
      • Guyader-Joly C.
      • Richard C.
      • Constant F.
      • Humblot P.
      • Ponsart C.
      • Hue I.
      • Grimard B.
      Energy and lipid metabolism gene expression of D18 embryos in dairy cows is related to dam physiological status.
      ).
      However, the embryo also contributes to the complexity of events that occur during preimplantation and this ultimately affects pregnancy outcome (
      • Ulbrich S.E.
      • Wolf E.
      • Bauersachs S.
      Hosting the preimplantation embryo: potentials and limitations of different approaches for analysing embryo-endometrium interactions in cattle.
      ). Approximately 5% of embryos die because of gross chromosomal abnormalities that prevent development (
      • Peters A.R.
      Embryo mortality in the cow.
      ), and oocyte developmental competence varies depending on which category of follicular environment they have been derived from (
      • Pavlok A.
      • Lucas-Hahn A.
      • Niemann H.
      Fertilization and developmental competence of bovine oocytes derived from different categories of antral follicles.
      ;
      • Lonergan P.
      • Monaghan P.
      • Rizos D.
      • Boland M.P.
      • Gordon I.
      Effect of follicle size on bovine oocyte quality and developmental competence following maturation, fertilization, and culture in vitro.
      ). As early as 1980, researchers reported variable length in bovine embryos recovered 15 d after superovulation from the same heifer (
      • Betteridge K.J.
      • Eaglesome M.D.
      • Randall G.C.B.
      • Mitchell D.
      Collection, description and transfer of embryos from cattle 10–16 days after oestrous.
      ). Those authors retransferred embryos with a range of sizes to recipients, which resulted in pregnancies from embryos as small as 2 mm on transfer to the largest (18 mm) embryo transferred; however, the input of the recipient was not well defined. We have noted in our previous studies that a range of conceptus lengths may be recovered from the same cow on gestational Day 14 or 15 from bulk transfer of IVP blastocysts (
      • Berg D.K.
      • van Leeuwen J.
      • Beaumont S.
      • Berg M.
      • Pfeffer P.L.
      Embryo loss in cattle between Days 7 and 16 of pregnancy.
      ). The trophectoderm can continue to elongate in vivo even without the embryonic disc, as demonstrated in a study where the discs were excised from tubular conceptuses before their transfer to a recipient (
      • Fléchon J.E.
      • Guillomot M.
      • Charlier M.
      • Flechon B.
      • Martal J.
      Experimental studies on the elongation of the ewe blastocyst.
      ). However, those cultured in vitro did not elongate further. As the amount of IFNT secreted by the embryo is consistent with the size of the trophectoderm tissue (
      • Robinson R.S.
      • Fray M.D.
      • Wathes D.C.
      • Lamming G.E.
      • Mann G.E.
      In vivo expression of interferon tau mRNA by the embryonic trophoblast and uterine concentrations of interferon tau protein during early pregnancy in the cow.
      ), the amount of IFNT present in the uterus available to signal pregnancy is therefore dependent on the growth rate of the embryo.
      In this study, we examined in detail the development of embryos on Day 15 using bulk transfer (n = 4 to 6 per cow) of Day 7 IVP blastocysts. Developmental differences between those nurtured in different maternal environments and any disparate development of those supported in an identical uterine environment (i.e., the same cow) were examined. The conceptus length, its trophectoderm gene expression, and embryonic disc development were compared to determine developmental variability. A mathematical model is proposed to calculate the early pre-attachment embryonic growth rate, encompassing both the embryonic and maternal factors.

      MATERIALS AND METHODS

      Animals

      All experimental procedures were undertaken in accordance with the regulations of the New Zealand Animal Welfare Act of 1999 under Ruakura Animal Ethics Committee approval AE12652. High breeding value Friesian cows (n = 37) in their second lactation were used to compare IVP embryo development at gestational Day 15 within the same uterine environment. The cows were maintained at the AgResearch Tokanui Farm under normal pastoral “best farm practice” grazing herd management plus silage as required to achieve a BCS of 5 (10-point scale) before calving. Following calving, the cows were subjected to various milking frequencies (0, 1, or 3 times per day), with feed intake and exercise manipulated to reduce the variation in BCS throughout the experiment. The animals were under veterinarian supervision throughout the experiment.

      Sequential Embryo Transfer and Recovery

      At approximately 28 to 30 d postpartum, the estrous cycles of the cows were synchronized using controlled internal drug releasing (CIDR) inserts (Zoetis, Auckland, New Zealand). The CIDR was inserted for a total of 12 d, with a single injection of a prostaglandin F analog (2 mL of 250 mg/mL cloprostenol sodium; Estroplan, Parnell Technologies, Alexandria, Australia) given on d 8. At the time of CIDR removal, cows were tail-painted and observed for estrous behavior, and an initial IVP transfer was performed on Day 7 after standing estrus (Day 0). Standard laboratory procedures were followed to generate IVP embryos (
      • Berg D.K.
      • van Leeuwen J.
      • Beaumont S.
      • Berg M.
      • Pfeffer P.L.
      Embryo loss in cattle between Days 7 and 16 of pregnancy.
      ), taking care to use ovaries from beef-Friesian cross heifers and frozen-thawed spermatozoa from one Friesian bull throughout the entire in vitro production. Different stage and grade blastocysts (early, n = 5; normal grade 1, n = 13; normal grade 2, n = 25; expanded grade 1, n = 57; expanded grade 2, n = 56; hatched blastocysts, n = 2) were selected for transfer on the basis of morphologic evaluation by the same experienced embryologist throughout the entire transfer period. From 4 to 6 of these blastocysts were bulk-transferred transcervically, ensuring that blastocysts with a mix of morphologies as even as possible were received by each recipient cow (each category had different numbers of blastocysts so a perfect match could not be achieved).
      Eight days after transfer, both the ipsilateral and contralateral uterine horns were nonsurgically flushed using an 18- or 20-French Foley 2-way embryo collection catheter as previously reported (
      • Berg D.K.
      • van Leeuwen J.
      • Beaumont S.
      • Berg M.
      • Pfeffer P.L.
      Embryo loss in cattle between Days 7 and 16 of pregnancy.
      ), and the contents of both uterine horns were collected into the same collection bottle. These embryos had their origin (cow) recorded and total length measured using an eyepiece graticule or a transparent ruler. In cases where embryos recovered were fragmented (25%), the actual number of embryos was confirmed by counting the visible ends under a stereomicroscope. They were also examined for the presence of an embryonic disc/epiblast (ED), which was photographed using a Nikon SMZ1500 microscope and DsFi1 camera (Nikon Instruments, Tokyo, Japan), and the total length and width of any ED were measured using a graticule. The ED area was calculated as the area of an ellipse (π × length × width/4). The ED were excised, the corresponding trophectoderm (TE) was placed in TRIzol (Invitrogen, Carlsbad, CA), and samples were stored at −80°C until processed.
      This experiment was repeated with a second IVP transfer at 86 d postpartum into the same recipient cows after a prostaglandin estrous synchronization, with the initial injection given at the time of embryo recovery from the first embryo transfer. A single injection of GnRH was given to induce ovulation 3 d later (d 0) and the second PGF injection given on d 12 to 15 of the subsequent estrous cycle. In this round, normal grade 1 and 2, expanded grade 1 and 2, and hatched blastocyst morphologies (n = 10, 17, 68, 64, and 11, respectively) were bulk transferred (n = 5 per cow) with an even mix of morphologies (to the extent possible) received by each recipient cow on the seventh day after expected estrus (d 0), as previously detailed. The embryos were collected using the same procedures as previously outlined.

      Progesterone Assay

      Blood was sampled from the tail vein into evacuated heparinized blood tubes (Vacutainer; Becton Dickinson, Auckland, New Zealand) on Days 2, 5, 7, and 15 of the embryo flush cycles for progesterone measurement. Blood samples were placed immediately in ice water, and then centrifuged at 4°C for 15 min at 1,500 × g. Aspirated plasma was stored at −20°C until assayed.
      Progesterone concentrations were measured with an electro chemiluminescence detection system (Elecsys Progesterone II kits, Roche Diagnostics GmbH, Mannheim, Germany) using an automated clinical immunology analyzer (Roche Modular E170, Hoffmann-La Roche Ltd., Basel, Switzerland) at New Zealand Veterinary Pathology Ltd. (Hamilton, New Zealand). The sensitivity of the assay was 0.03 ng·mL−1 and the co-efficient of variation was <5%. Only one sample had a concentration <0.03 ng·mL−1, and this measurement was assigned the value of the sensitivity of the assay (0.03 ng·mL−1).

      Mathematical Model of Embryo Development

      The mathematical model of embryo development combined the complex interaction between progesterone, which influences the uterine environment, and blastocyst developmental stage on transfer to the uterus. The model is based on the major biological mechanisms underlying embryo growth in the literature.
      The rate of change in the circulating progesterone concentration (P; ng·mL−1) is
      dPdt=kP(PmaxP),P(0)=P0,
      [1]


      where k is the rate of progesterone production (ng−1·mL·d−1), t is time from ovulation (d), P0 is the progesterone concentration on d 0 (ng·mL−1), and Pmax is the maximum progesterone concentration (
      • Shorten P.R.
      • Peterson A.J.
      • O'Connell A.R.
      • Juengel J.L.
      • McNatty K.P.
      • Soboleva T.K.
      A mathematical model of pregnancy recognition in mammals.
      ). This model describes the characteristics of the progesterone dynamics during the cycle (
      • Tsai S.J.
      • Wiltbank M.C.
      Prostaglandin F regulates distinct physiological changes in early and mid-cycle bovine corpora lutea.
      ).
      The production of IFNT is low during the first 13 d of pregnancy but by Day 15, there is a surge in IFNT production. The time and intensity of the IFNT signal can be modified by progesterone (
      • Satterfield M.C.
      • Bazer F.W.
      • Spencer T.E.
      Progesterone regulation of preimplantation conceptus growth and galectin 15 (LGALS15) in the ovine uterus.
      ). This modification is caused by progesterone-induced changes in the uterine environment rather than a direct effect on the embryo (
      • Clemente M.
      • de La Fuente J.
      • Fair T.
      • Al Naib A.
      • Gutierrez-Adan A.
      • Roche J.F.
      • Rizos D.
      • Lonergan P.
      Progesterone and conceptus elongation in cattle: a direct effect on the embryo or an indirect effect via the endometrium?.
      ). Elevated progesterone concentrations during the early luteal phase positively correlate with embryo survival, whereas low progesterone decreases survival (
      • Diskin M.G.
      • Morris D.G.
      Embryonic and early foetal losses in cattle and other ruminants.
      ;
      • Clemente M.
      • de La Fuente J.
      • Fair T.
      • Al Naib A.
      • Gutierrez-Adan A.
      • Roche J.F.
      • Rizos D.
      • Lonergan P.
      Progesterone and conceptus elongation in cattle: a direct effect on the embryo or an indirect effect via the endometrium?.
      ). To account for this effect, we defined a function h(t) (unitless) that describes uterine competence and is described by
      h(t)=aP(tb),
      [2]


      where a represents the intensity of the effect of progesterone on the competence of the endometrium (ng−1·mL), b represents the time delay between circulating progesterone and uterine competence (d), t is time from ovulation (d), and P(s) is the concentration (ng·mL−1) of progesterone at time s.
      Normally, the embryo takes approximately 5 d to travel from the fallopian tube to the uterus, where embryo growth is determined by the competence of the uterine environment (our results are not dependent on the value of 5 d). The rate of change in the embryo developmental stage (A) is described by
      dAdt=h1[1H(t5)]+h(t)n×H(t5),A(5)=A5,
      [3]


      where A5 is the embryo developmental stage on Day 5 (log10 cell number), h1 is the rate of embryo development (log10 cell number·d−1), n describes the nonlinear relationship between progesterone and embryo development (unitless), and H(t) denotes the Heaviside switch function:
      H(t)={1,t00,t<0.
      [4]


      Developmental stage is defined by log10 cell number before blastocyst hatching and by embryo length (mm) after blastocyst hatching, with embryo size increasing exponentially from Day 1 to blastocyst hatching on Day 9 (
      • Ushijima H.
      • Akiyama K.
      • Tajima T.
      Classification of morphological changes based on the number of cleavage divisions in bovine embryos.
      ). The cell doubling time from Day 5 is therefore inversely proportional to h(t)n (if n = 0.33, then doubling progesterone decreases the doubling time by 20%).
      Embryo length increases exponentially from blastocyst hatching on Day 9 (
      • Morris D.
      • Diskin M.G.
      Effect of progesterone on embryo survival.
      ;
      • Berg D.K.
      • van Leeuwen J.
      • Beaumont S.
      • Berg M.
      • Pfeffer P.L.
      Embryo loss in cattle between Days 7 and 16 of pregnancy.
      ). The rate of change in the log10 embryo length (L; log10 mm) is described by
      dLdt=+gh(t)n,L(tH)=LH,A(tH)=AH,
      [5]


      where embryo elongation is initiated at developmental stage AH (log10 cell number) at time tH (days), n describes the nonlinear relationship between progesterone and embryo elongation, and g is a measure of the rate of embryo elongation (log10 mm·d−1). The number of cells and length of a blastocyst at the time of hatching have been estimated (
      • Berg D.K.
      • van Leeuwen J.
      • Beaumont S.
      • Berg M.
      • Pfeffer P.L.
      Embryo loss in cattle between Days 7 and 16 of pregnancy.
      ;
      • Spencer T.E.
      Early pregnancy: Concepts, challenges, and potential solutions.
      ) and we assume that LH = log10(0.3) log10 mm and AH = log10(512) log10 cells.
      The size of each transferred blastocyst was not measured, and representative sizes were based on criteria derived from superovulated embryos, where the blastocyst stages were early (range 63–101 cells, mean 78.2 cells), normal (range 97–129 cells, mean 117.6 cells), expanding (range 142–193 cells, mean 159.2 cells), hatching (range 195–235 cells, mean 219.8 cells;
      • Ushijima H.
      • Akiyama K.
      • Tajima T.
      Classification of morphological changes based on the number of cleavage divisions in bovine embryos.
      ). Normal and expanding blastocysts were further classified as small or large and this was assumed to be based on the midpoint of the log10 cell number range (range 97–112 cells, mean 104.2; range 113–129 cells, mean 120.7; range 142–170 cells, mean 155.4; range 171–193 cells; mean 181.7). These sizes conform to exponential growth in embryo cell number and the estimated rate of embryo development (h1) is interpreted on this scale.

      Mathematical Model of Embryo Survival

      Several models of embryo survival exist in the literature and are described in detail below. Each model is based on a set of assumptions on the biology.

      Binomial Model

      Embryo survival is described by the probability (p) that an embryo survives from Day 7 to Day 15. The survival of embryos over this interval is assumed independent of the survival of other embryos (
      • Berg D.K.
      • van Leeuwen J.
      • Beaumont S.
      • Berg M.
      • Pfeffer P.L.
      Embryo loss in cattle between Days 7 and 16 of pregnancy.
      ). Embryo survival from Day 7 to Day 15 is therefore a binomial random variable. The probability that k out of n embryos survive in a cow (Q) is
      Q(k;n,p)=n!k!(nk)!pk(1p)nk,
      [6]


      where n!k!(nk)! is the number of possible ways of choosing k embryos from n.

      Mixed-Binomial Model

      The mixed-binomial model generalizes the binomial model (
      • Restall B.J.
      • Griffiths D.A.
      Assessment of reproductive wastage in sheep. 2. Interpretation of data concerning embryonic mortality.
      ). If the embryo survival probability (p) is a random variable (but constant for each cow) with E(p) = a, where E(p) denotes the expected value of the random variable p, and E(p2) = b [Var(p) = ba2], then the probability that k out of n embryos survive in a cow is
      Q(k;n,p)=n!k!(nk)!pk(1p)nkpN(a,ba2)
      [7]


      where N(μ,σ2) represents the normal distribution with mean μ and variance σ2. The variance in embryo survival probability [Var(p)] is the sum of a cow variance component (σ2c) and an embryo sampling variance component (σ2E/n) We note that the variance in the uniform probability distribution is 1/12, so that σE < 0.289.

      McMillan and Restall and Griffiths Model

      The
      • McMillan W.H.
      Statistical models predicting embryo survival to term in cattle after embryo transfer.
      and
      • Restall B.J.
      • Griffiths D.A.
      Assessment of reproductive wastage in sheep. 2. Interpretation of data concerning embryonic mortality.
      model allows for a subset of cows that are not able to maintain an embryo irrespective of the quality of the embryo. The probability that a cow is able to maintain an embryo is r [i.e., if there are N cows, then (1 − r)N cows are not able to maintain an embryo] and such cows are termed “receptive.” Cow receptiveness is therefore a Bernoulli random variable. This model allows both uterine receptiveness and embryo quality factors to be described and allows these dual components of the biology to be analyzed (
      • Berg D.K.
      • van Leeuwen J.
      • Beaumont S.
      • Berg M.
      • Pfeffer P.L.
      Embryo loss in cattle between Days 7 and 16 of pregnancy.
      ). The probability that k out of n embryos survive in a cow is
      Q(k;n,p,r)=(1r)δ(k)+rn!k!(nk)!pk(1p)nk,
      [8]


      where δ(k) = 1 if k = 0 and δ(k) = 0 if k ≥ 1, the probability that a cow is able to maintain a pregnancy is r, and p is a measure of embryo viability. It is assumed that the viabilities of individual embryos in the same uterus are independent. It is important to note that this model can be interpreted as a special case of the mixed-binomial model when a = pr and b = p2r.

      Mixed McMillan and Restall and Griffiths Model

      The McMillan model can be extended to allow for variability in embryo viability between animals. The probability that k out of n embryos survive in a cow is
      Q(k;n,p,r)=(1r)δ(k)+rn!k!(nk)!pk(1p)nkpN(p˜,τ2)
      [9]


      where δ(k) = 1 if k = 0 and δ(k) = 0 if k ≥ 1, the probability that a cow is able to maintain a pregnancy is r, N(μσ2) is the normal distribution with mean μ and variance σ2, p˜ is the expected embryo viability, and τ2 is the variance in embryo viability. This model is a special case of the mixed-binomial model when r = 1.

      Progesterone-Dependent Embryo Survival Model

      The mixed McMillan model can be extended to allow for progesterone-dependent effects on embryo viability. The probability that k out of n embryos survive in a cow is
      Q(k;n,p,r,P(tP))=(1r)δ(k)+rn!k!(nk)!(p*)k(1p*)nkp*=p+βp,1P(tP)+βp,2P(tP)2+βEBEB+βA7A7+i=1MβgeneigeneipN(p˜,τ2)
      [10]


      where δ(k) = 1 if k = 0 and δ(k) = 0 if k ≥ 1, the probability that a cow is able to maintain a pregnancy is r, N(μ,σ2) is the normal distribution with mean μ and variance σ2, P(tP) is the progesterone concentration at time tP defined by Eq. [1], p˜ is the expected embryo viability, τ2 is the variance in embryo viability, βp,1p,2 denote linear and quadratic coefficients for the effect of progesterone on embryo viability, EB is energy balance (MJ·d−1), βEB denotes the linear effect of energy balance on embryo viability, A7 is the developmental stage of the transferred embryo on Day 7 (log10 cell number), and βA7 denotes the effect of the developmental stage of the transferred Day 7 embryo on embryo viability, gene denotes the Day 15 embryo gene expression for the ith gene [log10 (relative copy number × 103)], βgenei denotes the effect of Day 15 gene expression for the ith gene on embryo viability, and M denotes the number of measured genes. This model can be readily extended to include other factors (continuous or categorical) that regulate embryo viability. The progesterone-dependent regression coefficients are sufficiently small that a logistic transformation is not required in the model.

      Modeling Energy Balance

      Cow daily energy balance (EB; MJ·d−1) was calculated according to a modification of the procedure detailed in
      • Pryce J.E.
      • Harris B.L.
      • Montgomerie W.A.
      • Jackson R.
      • Macdonald K.A.
      • Glassey C.B.
      • Thorrold B.S.
      • Holmes C.W.
      Comparing feed allowances to inferred energy intake using data from a dairy grazing farm trial.
      . The method was modified so that changes in BCS and liveweight both affect energy balance (
      • AFRC
      Energy and Protein Requirements of Ruminants. An advisory manual prepared by the AFRC Technical Committee on Responses to Nutrients.
      ,
      • Gregory N.G.
      • Robins J.K.
      • Thomas D.G.
      • Purchas R.W.
      Relationship between body condition score and body composition in dairy cows.
      ). Daily EB (MJ·d−1) on day t was calculated as
      EBt=MEintaket(MEexerciset+MEmaint+MEmilkt+MEbcst+MEbcnft),
      [11]


      where MEintake is the measured intake energy (based on the daily sum of pasture ME and supplement ME calculated from pasture analysis), MEexercise is the measured energy expenditure due to exercise (based on measured daily distance walked and 2 MJ of ME km−1 walked on flat land to the milking platform and 3 MJ of ME km−1 walking rolling terrain), MEmain is the energy requirement for maintenance, MEmilk is the energy requirement for milk, MEbcs is the energy requirement for change in BCS, and MEbcnf is the energy requirement for change in body content nonfat. An assessment of pasture DMI was performed for each treatment during the experimental period using the rising plate meter (Farmworks, Palmerston North, New Zealand) technique. This involved a daily assessment of pre- and post-grazing pasture mass. The average DMI of pasture consumed per animal was calculated as the difference between the pre- and post-grazing pasture mass, multiplied by the area offered (meters), and then divided by the number of cows in the group. Pasture samples were collected by taking a minimum of 10 cuts to 5 cm above the ground at random intervals across the paddock and submitted for analysis every 2 wk (Hills Laboratory, Hamilton, New Zealand) to determine pasture ME intake. The equations are
      MEmaint=0.53km(LWTt1.08)0.67MEmilkt=1kl(34.8Fatt+22.3Prott+19.9Lactt0.108Volt)BCFt=1100(1.1043+1.7541×BCSt)×(0.8117×LWTt)MEbcft=Efatkg(BCFtBCFt1)BCNFt=0.8117×LWTtBCFtMEbcnft=Enfatkg(BCNFtBCNFt1)
      [12]


      where t is time (d), BCF denotes the body content of fat (kg), BCNF denotes the body content nonfat (kg), LWT is liveweight (kg), empty BW is assumed to be 81.17% of liveweight (
      • Gregory N.G.
      • Robins J.K.
      • Thomas D.G.
      • Purchas R.W.
      Relationship between body condition score and body composition in dairy cows.
      ), Fat, Prot, Lact, and Vol are the total daily fat, protein, lactose, and volume yields (kg), respectively, the heat of combustion for body fat is Efat = 39.33 MJ·kg−1, the heat of combustion for body nonfat is Enfat = 21.83 MJ·kg−1, the efficiency of energy for growth is kg (= 0.55), the efficiency of energy for maintenance is km (= 0.678), and the efficiency of energy for lactation is kl (= 0.6;
      • AFRC
      Energy and Protein Requirements of Ruminants. An advisory manual prepared by the AFRC Technical Committee on Responses to Nutrients.
      ). Intake, exercise (walking distances), and milk yield (in-line milk meters) were measured daily. Milk composition was measured weekly, and LWT and BCS were measured weekly by a single observer, and these were interpolated with a shape-preserving piecewise cubic interpolation to obtain daily estimates.

      Model-Fitting Procedure

      The model equations (Eq. [15]) were fitted to the multi-response data (progesterone and log10 embryo length) using nonlinear regression (
      • Bates D.M.
      • Watts D.G.
      Nonlinear Regression Analysis and its Applications.
      ). Models were first calibrated to literature data and then validated using our data. The variances of the deviations in measurements within response variables were assumed constant, possibly dependent, and allowed for the variances in measurement deviations to be different between response variables. Embryo length measurements were log-transformed for model fitting. A weighted least squares procedure was used when standard errors on measurements were available. Identifiability analyses were performed to ensure that the estimated model parameters were unique.
      Differential equations were solved using ode15s in MATLAB (The MathWorks, Natick, MA). Markov chain Monte Carlo (MCMC) was used to determine the standard errors in the model parameters (
      • Gilks W.R.
      • Richardson A.
      • Spiegelhalter D.J.
      Markov Chain Monte Carlo in Practice.
      ). A likelihood ratio test was used to compare nested models (
      • Bates D.M.
      • Watts D.G.
      Nonlinear Regression Analysis and its Applications.
      ).

      Embryo Analysis

      Trophectoderm expression of 9 genes temporally expressed in embryonic development was examined by quantitative reverse transcription (RT) PCR. These were trophectoderm cell-specific: IFNT, trophoblast Kunitz domain protein 1 (TKDP1), dickkopf 1 (DKK1), pregnancy-associated glycoprotein 11 (PAG11); or trophoblast binucleate cell specific: bovine placental lactogen (CSH2, previously bPL), prolactin-related protein 1 (PRP1), and PAG9. Podoplanin (PDPN), identified from an in-house embryonic RNASeq analysis as upregulated in Day 14 embryos, was quantified, as well as prostaglandin G/H synthase 2 (PTGS2), whose enriched expression in blastocysts has been correlated with pregnancy success (
      • Ghanem N.
      • Salilew-Wondim D.
      • Gad A.
      • Tesfaye D.
      • Phatsara C.
      • Tholen E.
      • Looft C.
      • Schellander K.
      • Hoelker M.
      Bovine blastocysts with developmental competence to term share similar expression of developmentally important genes although derived from different culture environments.
      ).
      Reverse transcription of RNA extracted from the TE stored in TRIzol was as previously described (
      • Smith C.S.
      • Berg D.K.
      • Berg M.
      • Beaumont S.
      • Standley N.T.
      • Wells D.N.
      • Pfeffer P.L.
      Simultaneous gene quantitation of multiple genes in individual bovine nuclear transfer blastocysts.
      ). Briefly, the RNA was extracted using chloroform-isoproanol from stored samples with MS2 RNA (Roche, Mannheim, Germany) and linear acrylamide (Ambion, Austin, TX) carriers followed by removal of any remaining DNA with RNase-free DNase1 (Invitrogen, Carlsbad, CA). Reverse transcription was performed with oligo dT20 anchored primer, RNase OUT inhibitor, and Superscript III (Invitrogen). An RT negative control was included.
      Quantification of RNA was conducted via SYBR Green-based RT-PCR using a Corbett Rotor-Gene 600 machine with 10-µL reactions containing 5 µL of TaKaRa Sybr Premix Ex Taq mix (Takara Bio Inc., Otsu, Japan), 0.1 µM each primer, and 2 µL of template (
      • Ledgard A.M.
      • Lee R.S.
      • Couldrey C.
      • Peterson A.J.
      Dickkopf-1 expression during early bovine placentation and its down-regulation in somatic cell nuclear transfer (SCNT) pregnancies.
      ). The thermal program involved a 1-min activation incubation at 95°C followed by 40 cycles of 95°C for 10 s, an annealing temperature of 60°C for 15 s, and extension at 60°C for 20 s, with a ramp speed of 20°C s−1. A no-template control, an RT-negative control, and an RT-positive control were included in each run. The PCR products were sequenced (University of Waikato, Hamilton, New Zealand) to verify correct identity (Table 1). Values are expressed as the relative copy number (RCN) normalized against the geometric mean of 3 internal housekeeping controls (GAPDH, RPL19, and UBE2K) for each sample (
      • Wilkening S.
      • Bader A.
      Quantitative real-time polymerase chain reaction: Methodical analysis and mathematical model.
      ).
      Table 1Quantitative real-time reverse transcription-PCR primer sequences
      Gene symbolAccession no.Primer sequence 5′ to 3′ (forward, reverse)
      CSH2J02840GTTCATCAACAGCTGCCACA

      GGATGGATCATCACTAACCA
      DKK1XM_580572CAGTGTGGCACTTACCTGTA

      GGGGGAAGGGTTTTACAT
      GAPDHBC102589CTCCCAACGTGTCTGTTGTG

      TGAGCTTGACAAAGTGGTCG
      IFNTNM_001015511.3GCTATCTCTGTGCTCCATGAGATG

      AGTGAGTTCAGATCTCCACCCATC
      PAG9BC123608TCCTTTTGTACCATGCCAGC

      TGCCCTCCTGCTTGTTTTTC
      PAG11NM_176623.2CCCAAACCAAAAGCTGGCTAATAA

      ATCGATGCCATTGATGGTGAA
      PDPNNM_001033120.1TGGCTACGGAGCTTTTTCAT

      CACACCCAGGGTTGTTTTCT
      PRP1NM174443TGGTCATCAAAATGTACGTGGT

      AGTAGACAAAGCCCAGGAACAG
      PTGS2AF031698TAGAATCCTGTTCGGGTACAGTCAC

      TCCTTGCTGTTCCCATCCATGT
      RPL19XM_002695953.3CCAGTGTCCTTCGCTGTGGCA

      GGCATCGAGCCCGGGAATGG
      TKDP1NM_205776.1CATACACTAGAGGAATTCCCAA

      TGCTGAGTATTCAATCTTGAGTG
      UBE2KBC142324CAGCGAATCAAGCGGGAGTT

      GCCCCTGTGACGGAACTAA

      Statistical Analysis

      The Akaike information criterion (AIC) was used to determine the best model to describe embryo survival. The AIC is an objective method for selection of the best model for data analysis (
      • Burnham K.P.
      • Anderson D.R.
      Model Selection and Multimodel Selection.
      ) and has been used to compare different embryo survival models to data (
      • Roberts S.A.
      • Hirst W.M.
      • Brison D.R.
      • Vail A.
      Embryo and uterine influences on IVF outcomes: An analysis of a UK multi-centre cohort.
      ;
      • Shorten P.R.
      • O'Connell A.R.
      • Demmers K.J.
      • Edwards S.J.
      • Cullen N.G.
      • Juengel J.L.
      Effect of age, weight, and sire on embryo and fetal survival in sheep.
      ). Model parameters and their standard errors were estimated using maximum likelihood (
      • Pawitan Y.
      In all likelihood: Statistical modelling and inference using likelihood.
      ). The data were also analyzed using generalized linear models and generalized linear mixed models with binomial distribution and logit link. Model residuals were analyzed for homoscedasticity and normality. Calculations were performed in R and Matlab (The Mathworks).
      Relationships between TE length, ED length/area, and gene expression were determined on log-transformed data. Multivariate linear regression was also used to investigate the effect of progesterone, EB, and embryo transfer size on the gene expression, ED size, and TE length on Day 15 embryos. The error variance covariance matrix was assumed to be unstructured (correlated and heteroscedastic). The model represents a continuous response vector (d-dimensional) as a linear combination of predictors (K − 1) and a multivariate normal (MVN)-distributed error vector. For the ith observation (yi), given the design matrix Xi (d × K) and the vector of regression coefficients β (K × 1), the multivariate linear regression model for the response vector (d × 1) is
      yi=Xiβ+ɛi,ɛiMVNd(0,),
      [13]


      where the errors (εi) are assumed independent between observations and multivariate normal distributed with variance-covariance matrix Σ (
      • Rencher A.C.
      Methods of Multivariate Analysis.
      ). The regression coefficients and error variance-covariance matrix were estimated using maximum likelihood. Standard errors were calculated according to the inverse of the observed Fisher information matrix. An expectation/conditional maximization algorithm was used to impute missing response values for gene expression (4 out of 296 gene expression measurements over the 6 major genes of interest) and ED size (n = 4 embryos). Model residuals were tested to be independent, with a multivariate normal distribution.

      RESULTS AND DISCUSSION

      Embryo Recoveries

      One hundred sixty-seven embryos were recovered from 55 of 66 flushing events completed at Day 15 of gestation, and the remaining 11 flushings were considered nonpregnant. From 13 of these flushings, only a single embryo was recovered from the bulk transfer of 4 to 6 blastocysts 8 d earlier. However, multiple embryos of very similar lengths were recovered from 19 flushings, and multiple embryos of varying lengths were recovered from 23 flushings. The length of intact conceptuses was between 0.34 and 170 mm; however, in some cases, precise measurement of TE length was not possible because of conceptus damage during the recovery process (n = 15). The average length of recovered embryos was 1.18 log10 mm, with a standard deviation of 0.68 log10 mm (mean of 52 mm). Based on developmental stage, the predicted average number of cells in the transferred embryos was 2.19 log10 cells with a standard deviation of 0.09 log10 cells (mean of 158 cells).

      Modeling Embryo Growth

      Calibration of the Progesterone Model to Literature Data

      The progesterone model (Eq. [1]) predicted progesterone measured daily on Day 1 to 14 by other researchers (
      • Tsai S.J.
      • Wiltbank M.C.
      Prostaglandin F regulates distinct physiological changes in early and mid-cycle bovine corpora lutea.
      ;
      • Mann G.E.
      • Fray M.D.
      • Lamming G.E.
      Effects of time of progesterone supplementation on embryo development and interferon-τ production in the cow.
      ;
      • Clemente M.
      • de La Fuente J.
      • Fair T.
      • Al Naib A.
      • Gutierrez-Adan A.
      • Roche J.F.
      • Rizos D.
      • Lonergan P.
      Progesterone and conceptus elongation in cattle: a direct effect on the embryo or an indirect effect via the endometrium?.
      ;
      • Forde N.
      • Beltman M.E.
      • Duffy G.B.
      • Duffy P.
      • Mehta J.P.
      • O'Gaora P.
      • Roche J.F.
      • Lonergan P.
      • Crowe M.A.
      Changes in the endometrial transcriptome during the bovine estrous cycle: effect of low circulating progesterone and consequences for conceptus elongation.
      ) with good accuracy (R2 = 0.99). The progesterone model also provided a good prediction of progesterone concentration on Day 7 and over Days 2, 5, 7 and 15 combined (R2 = 0.99). This is demonstrated for the
      • Tsai S.J.
      • Wiltbank M.C.
      Prostaglandin F regulates distinct physiological changes in early and mid-cycle bovine corpora lutea.
      progesterone dynamics in that 4 progesterone measurements (on Days 2, 5, 7, and 15) can be utilized by the model (Eq. [1]) to provide a good prediction of progesterone on Days 1 to 15 (Figure 1). We also found that the estimated model parameters for progesterone dynamics (
      • Tsai S.J.
      • Wiltbank M.C.
      Prostaglandin F regulates distinct physiological changes in early and mid-cycle bovine corpora lutea.
      ;
      • Mann G.E.
      • Fray M.D.
      • Lamming G.E.
      Effects of time of progesterone supplementation on embryo development and interferon-τ production in the cow.
      ;
      • Clemente M.
      • de La Fuente J.
      • Fair T.
      • Al Naib A.
      • Gutierrez-Adan A.
      • Roche J.F.
      • Rizos D.
      • Lonergan P.
      Progesterone and conceptus elongation in cattle: a direct effect on the embryo or an indirect effect via the endometrium?.
      ;
      • Forde N.
      • Beltman M.E.
      • Duffy G.B.
      • Duffy P.
      • Mehta J.P.
      • O'Gaora P.
      • Roche J.F.
      • Lonergan P.
      • Crowe M.A.
      Changes in the endometrial transcriptome during the bovine estrous cycle: effect of low circulating progesterone and consequences for conceptus elongation.
      ) based on a subset of the progesterone data (Days 2, 5, 7, and 15) were not significantly different from the estimated model parameters using the full progesterone data (Days 1–14).
      Figure thumbnail gr1
      Figure 1The estimated model progesterone dynamics based on the full progesterone data (Day 1–14; ×, solid line) or based on a subset of the progesterone data (Days 2, 5, 7, and 15; ○, dotted line) using data from
      • Tsai S.J.
      • Wiltbank M.C.
      Prostaglandin F regulates distinct physiological changes in early and mid-cycle bovine corpora lutea.
      .

      Calibration of the Embryo Growth Model to Literature Data

      The embryo growth (EG) model (Eq. [15]) was fitted to a mix of data from different laboratories and countries regarding the effect of circulating progesterone on embryo length at Days 14 to 16 (
      • Mann G.E.
      • Fray M.D.
      • Lamming G.E.
      Effects of time of progesterone supplementation on embryo development and interferon-τ production in the cow.
      ;
      • Clemente M.
      • de La Fuente J.
      • Fair T.
      • Al Naib A.
      • Gutierrez-Adan A.
      • Roche J.F.
      • Rizos D.
      • Lonergan P.
      Progesterone and conceptus elongation in cattle: a direct effect on the embryo or an indirect effect via the endometrium?.
      ;
      • Forde N.
      • Beltman M.E.
      • Duffy G.B.
      • Duffy P.
      • Mehta J.P.
      • O'Gaora P.
      • Roche J.F.
      • Lonergan P.
      • Crowe M.A.
      Changes in the endometrial transcriptome during the bovine estrous cycle: effect of low circulating progesterone and consequences for conceptus elongation.
      ;
      • O'Hara L.
      • Forde N.
      • Duffy P.
      • Randi F.
      • Kelly A.K.
      • Valenza A.
      • Rodriguez P.
      • Lonergan P.
      Effect of combined exogenous progesterone with luteotrophic support via equine chorionic gonadotrophin (eCG) on corpus luteum development, circulating progesterone concentrations and embryo development in cattle.
      ), providing a description of embryo growth in an average cow. Over the 8 experiments in these studies, the ability of the EG model to predict embryo length is shown in Figure 2A [R2 = 0.73 (0.14, 0.95), where the values in parentheses denote a 95% CI; n = 8]. The estimated model parameters are a = 0.018 ± 0.002 ng−1·mL, b = 4.75 ± 0.16 d, and n = 0.42 ± 0.02 (assuming g = 1 because the data does not allow for g to be estimated independently and g = 1 corresponds to equal cell dividing time pre- and post-blastocyst hatching). The EG model was also calibrated on a separate data set (
      • O'Hara L.
      • Forde N.
      • Kelly A.K.
      • Lonergan P.
      Effect of bovine blastocyst size at embryo transfer on day 7 on conceptus length on day 14: Can supplementary progesterone rescue small embryos?.
      ,
      • O'Hara L.
      • Forde N.
      • Carter F.
      • Rizos D.
      • Maillo V.
      • Ealy A.D.
      • Kelly A.K.
      • Rodriguez P.
      • Isaka N.
      • Evans A.C.O.
      • Lonergan P.
      Paradoxical effect of supplementary progesterone between Day 3 and Day 7 on corpus luteum function and conceptus development in cattle.
      ) that displayed improved embryo growth characteristics (independent of treatments) to better ascertain the underlying reasons for this improved growth. The ability of the model to predict embryo length in these further 8 experiments is shown in Figure 2B [R2 = 0.87 (0.43, 0.98); n = 8]. The estimated EG model parameters are a = 0.047 ± 0.006 ng−1·mL, b = 5.24 ± 0.29 d, and n = 0.46 ± 0.03 (assuming g = 1). The embryo growth parameter a was significantly greater in
      • O'Hara L.
      • Forde N.
      • Kelly A.K.
      • Lonergan P.
      Effect of bovine blastocyst size at embryo transfer on day 7 on conceptus length on day 14: Can supplementary progesterone rescue small embryos?.
      ,
      • O'Hara L.
      • Forde N.
      • Carter F.
      • Rizos D.
      • Maillo V.
      • Ealy A.D.
      • Kelly A.K.
      • Rodriguez P.
      • Isaka N.
      • Evans A.C.O.
      • Lonergan P.
      Paradoxical effect of supplementary progesterone between Day 3 and Day 7 on corpus luteum function and conceptus development in cattle.
      ) than the mix of data in the earlier experiments (Figure 2A, P < 0.001), which is consistent with altered embryo growth in the group of cows studied by
      • O'Hara L.
      • Forde N.
      • Kelly A.K.
      • Lonergan P.
      Effect of bovine blastocyst size at embryo transfer on day 7 on conceptus length on day 14: Can supplementary progesterone rescue small embryos?.
      ,
      • O'Hara L.
      • Forde N.
      • Carter F.
      • Rizos D.
      • Maillo V.
      • Ealy A.D.
      • Kelly A.K.
      • Rodriguez P.
      • Isaka N.
      • Evans A.C.O.
      • Lonergan P.
      Paradoxical effect of supplementary progesterone between Day 3 and Day 7 on corpus luteum function and conceptus development in cattle.
      ). Parameters b and n were not significantly different between the 2 data sets. The ability of the EG model to predict embryo length in all 16 experiments combined (Figure 2A, B) is R2 = 0.81 (0.53, 0.93).
      Figure thumbnail gr2
      Figure 2The ability of the embryo growth model (]) to predict the effect of circulating progesterone (A) on embryo length on Day 14–16 (R2 = 0.73) using data from
      • Mann G.E.
      • Fray M.D.
      • Lamming G.E.
      Effects of time of progesterone supplementation on embryo development and interferon-τ production in the cow.
      ,
      • Clemente M.
      • de La Fuente J.
      • Fair T.
      • Al Naib A.
      • Gutierrez-Adan A.
      • Roche J.F.
      • Rizos D.
      • Lonergan P.
      Progesterone and conceptus elongation in cattle: a direct effect on the embryo or an indirect effect via the endometrium?.
      ,
      • Forde N.
      • Beltman M.E.
      • Duffy G.B.
      • Duffy P.
      • Mehta J.P.
      • O'Gaora P.
      • Roche J.F.
      • Lonergan P.
      • Crowe M.A.
      Changes in the endometrial transcriptome during the bovine estrous cycle: effect of low circulating progesterone and consequences for conceptus elongation.
      , and
      • O'Hara L.
      • Forde N.
      • Duffy P.
      • Randi F.
      • Kelly A.K.
      • Valenza A.
      • Rodriguez P.
      • Lonergan P.
      Effect of combined exogenous progesterone with luteotrophic support via equine chorionic gonadotrophin (eCG) on corpus luteum development, circulating progesterone concentrations and embryo development in cattle.
      ; (B) on embryo length on Day 14–16 (R2 = 0.87) using data from
      • O'Hara L.
      • Forde N.
      • Kelly A.K.
      • Lonergan P.
      Effect of bovine blastocyst size at embryo transfer on day 7 on conceptus length on day 14: Can supplementary progesterone rescue small embryos?.
      ,
      • O'Hara L.
      • Forde N.
      • Carter F.
      • Rizos D.
      • Maillo V.
      • Ealy A.D.
      • Kelly A.K.
      • Rodriguez P.
      • Isaka N.
      • Evans A.C.O.
      • Lonergan P.
      Paradoxical effect of supplementary progesterone between Day 3 and Day 7 on corpus luteum function and conceptus development in cattle.
      ); (C) the size of transferred embryo on average recovered embryo length on Day 15 (R2 = 0.52; n = 55 cows); and (D) the size of transferred embryo on the length of individual embryos on Day 15 (R2 = 0.47; n = 43 embryos). Error bars denote SEM.

      Validation of the EG Model with our Data

      The EG model was fitted to the data for each cow regarding the effect of circulating progesterone and the developmental morphology of the transferred blastocyst on the average recovered embryo length on Day 15. We observed a tendency (P = 0.1) for decreased growth as a larger number of embryos (n = 4, 5, 6) were transferred. Embryo size on Day 15 was dependent on progesterone (P < 0.01) and developmental stage on Day 7 (P < 0.05). The ability of the model to predict the average recovered embryo length is shown in Figure 2C [R2 = 0.52 (0.32, 0.69); n = 55]. The estimated model parameters were a = 0.0165 ± 0.001 ng−1·mL and n = 0.466 ± 0.02 (assuming g = 1 and b = 4.75 d). The estimated embryo growth parameters (a, n) were not significantly different from those for the mix of data (Figure 2A); however, the embryo growth parameter a was significantly greater in the
      • O'Hara L.
      • Forde N.
      • Kelly A.K.
      • Lonergan P.
      Effect of bovine blastocyst size at embryo transfer on day 7 on conceptus length on day 14: Can supplementary progesterone rescue small embryos?.
      ,
      • O'Hara L.
      • Forde N.
      • Carter F.
      • Rizos D.
      • Maillo V.
      • Ealy A.D.
      • Kelly A.K.
      • Rodriguez P.
      • Isaka N.
      • Evans A.C.O.
      • Lonergan P.
      Paradoxical effect of supplementary progesterone between Day 3 and Day 7 on corpus luteum function and conceptus development in cattle.
      ) data (Figure 2B). A reduced model of only the effect of progesterone on embryo length on Day 15 (based on average transferred blastocyst size) explained a smaller proportion of the variance in embryo length (R2 = 0.47). The EG model was also able to predict the length of individual embryos for cows with full recovery of all transferred embryos (Figure 2D; R2 = 0.47, n = 43), assuming that the order of embryos (based on size) is not likely to change within a cow between Day 7 and Day 15, although stochastic effects may change this order in a particular cow. Such stochastic effects in the growth process (based on the difference in the variance estimates) can be modeled using stochastic differential equations similar to those developed for modeling stochastic growth in microbiology applications (
      • Shorten P.R.
      • Soboleva T.K.
      • Pleasants A.B.
      • Membre J.-M.
      A risk assessment approach applied to the growth of Erwinia carotovora in vegetable juice for variable temperature conditions.
      ). However, the standard deviation in the measured embryo length on Day 15 (0.52 ± 0.06 log10 mm) was not significantly different from that in the predicted embryo length on Day 15 (0.43 ± 0.05 log10 mm) based on the deterministic EG model and Day 7 embryo size (Figure 2D; P = 0.2). This indicates that stochastic effects in growth that change the order of embryo size within a cow are relatively small, as large stochastic growth effects would generate a significantly larger standard deviation in measured embryo length on Day 15. Thus, modeling using stochastic differential equations was not necessary.
      Others have shown a clear relationship between the kinetics of development of early bovine embryos to first cleavage after insemination and developmental competence (
      • Holm P.
      • Shukri N.N.
      • Vajta G.
      • Booth P.
      • Bendixen C.
      • Callesen H.
      Developmental kinetics of the first cell cycles of bovine in vitro produced embryos in relation to their in vitro viability and sex.
      ,
      • Holm P.
      • Booth P.J.
      • Callesen H.
      Kinetics of early in vitro development of bovine in vivo- and in vitro-derived zygotes produced and/or cultured in chemically defined or serum-containing media.
      ;
      • Lonergan P.
      • Khatir H.
      • Piumi F.
      • Rieger D.
      • Humblot P.
      • Boland M.P.
      Effect of time interval from insemination to first cleavage on the developmental characteristics, sex ratio and pregnancy rate after transfer of bovine embryos.
      ). However, we found that although Day 15 embryo size is dependent on the specific morphological stage (indicative of cell number or size) of the Day 7 blastocyst when it was transferred, progesterone is a more important factor than transferred embryo size on subsequent growth. The fact that our EG model was able to predict embryo lengths in cases where all embryo had been recovered, on the stated assumption that the order of embryos based on size is not likely to change, suggests that this assumption may be correct.

      The Role of EB on Embryo Growth in our Data

      We found no effect of average EB from 40 d before transfer to recovery on progesterone on Day 2 (P = 0.5), Day 7 (P = 0.9), or Day 15 (P = 0.6). Lower average energy balance over the 40 d before transfer was associated with reduced embryo growth to Day 15 [βEB = 0.0043 ± 0.0021 log10 mm (MJ·d−1)−1; P < 0.05] and this energy balance effect is independent of progesterone (the EB effect remains when progesterone is included as a covariate in the model; i.e., it cannot be explained by progesterone). Lower EB over the period from transfer to recovery was also associated with reduced embryo growth to Day 15 [βEB = 0.003 ± 0.0014 log10 mm (MJ·d−1)−1; P < 0.05] and this EB effect is independent of progesterone. Average EB from 40 d before transfer is moderately correlated with average EB from transfer to recovery (R = 0.5) and this makes it difficult to distinguish between EB effects before and after embryo transfer. The effect of average EB (MJ·d−1) before transfer on embryo growth to Day 15 is not significantly different from the effect of average EB after transfer on embryo growth to Day 15 (P = 0.6). Furthermore, the effect of cumulative EB (MJ) before transfer on embryo growth to Day 15 was not significantly different from the effect of cumulative EB (MJ) after transfer on embryo growth to Day 15 (P = 0.4). This observation is a component of the association between lower EB and reduced pregnancy rate (
      • Roche J.R.
      • Burke C.R.
      • Meier S.
      • Walker C.G.
      Nutrition x reproduction interaction in pasture-based systems: Is nutrition a factor in reproductive failure?.
      ). Our findings are complementary to the association between negative energy balance and impaired follicular development (
      • Beam S.W.
      • Butler W.R.
      Energy balance and ovarian follicle development prior to the first ovulation postpartum in dairy cows receiving three levels of dietary fat.
      ) and highlight that both embryonic and uterine factors are regulated by EB. The intrinsic capability of the blastocyst is an initial driver of early pregnancy loss when development blocks or is slow at the blastocyst stage; otherwise, the uterine environment, driven by progesterone and EB, is a more important component in the stimulation of embryonic growth.

      Embryo Survival

      Embryo Survival Model Selection for Inference Based on our Data

      The AIC provides an objective criterion for selection of the best model for data analysis. The best model was Eq. [10] (AIC = 112.917), followed by Eq. [9] (AIC = 118.295), Eq. [7] (AIC = 118.477), Eq. [8] (AIC = 125.366), and Eq. [6] (AIC = 140.221). This indicates that embryo survival can be considered by a model in which cow receptiveness is a Bernoulli random variable, embryo viability is a binomial random variable, and the embryo survival probability is progesterone-dependent and variable between cows. We therefore used Eq. [10] for data inference in this section.

      Embryo Survival for our Data (All Cows)

      The effect of number of embryos transferred (4, 5, or 6) on embryo survival probability (p in Eq. [10]) was not significant. This is consistent with the findings of
      • Berg D.K.
      • van Leeuwen J.
      • Beaumont S.
      • Berg M.
      • Pfeffer P.L.
      Embryo loss in cattle between Days 7 and 16 of pregnancy.
      , who only observed an effect of number of transferred embryos on embryo survival over this period when >20 embryos were transferred. The estimated survival probability for an individual embryo is p = 0.51 ± 0.04 (Eq. [10]). Day 15 embryos <2 mm have been successfully retransferred resulting in a calf (
      • Betteridge K.J.
      • Eaglesome M.D.
      • Randall G.C.B.
      • Mitchell D.
      Collection, description and transfer of embryos from cattle 10–16 days after oestrous.
      ), suggesting that our estimates of the embryo survival probability of an individual embryo (p = 0.51 ± 0.04) are not significantly biased. There was a significant effect of progesterone on Day 7 on embryo survival probability from Day 7 to 15 [Eq. [10], Figure 3; βp,1 = 0.054 ± 0.017 (ng·mL−1)−1; P < 0.01]. There was no quadratic effect of progesterone on embryo survival, although embryo survival tended to be lower for high progesterone on Day 7 (P = 0.1, Eq. [10]). This trend is consistent with
      • Stronge A.J.H.
      • Sreenan J.M.
      • Diskin M.G.
      • Mee J.F.
      • Kenny D.A.
      • Morris D.G.
      Post insemination milk progesterone concentration and embryo survival in dairy cows.
      , who observed a significant negative quadratic relationship between milk progesterone on Day 7 and embryo survival. Progesterone on Day 7.8 ± 1.5 was the best predictor of embryo survival (based on Eq. [1] and]10]). Given the ∼2-d delay between circulating progesterone and progesterone-induced changes in the uterine environment in which the embryo is developing (
      • Clemente M.
      • de La Fuente J.
      • Fair T.
      • Al Naib A.
      • Gutierrez-Adan A.
      • Roche J.F.
      • Rizos D.
      • Lonergan P.
      Progesterone and conceptus elongation in cattle: a direct effect on the embryo or an indirect effect via the endometrium?.
      ), this suggests that progesterone-dependent effects on embryo survival are greatest on Day 9.8 ± 1.5. We detected no effect of developmental stage of the transferred embryo on embryo survival probability to Day 15 (Eq. 10). There was also no effect of average EB from 40 d before transfer to recovery on embryo survival to Day 15: βEB = 0.00064 ± 0.0011 (MJ·d−1)−1; P = 0.6, Eq. [10]. The estimated standard deviation in embryo survival between cows is at least σC = 0.22 ± 0.04 (assuming σE < 0.289; P < 0.01). This is consistent with the between-animal variance in embryo/fetal survival in sheep (
      • Shorten P.R.
      • O'Connell A.R.
      • Demmers K.J.
      • Edwards S.J.
      • Cullen N.G.
      • Juengel J.L.
      Effect of age, weight, and sire on embryo and fetal survival in sheep.
      ).
      Figure thumbnail gr3
      Figure 3The effect of progesterone on Day 7.8 on the probability of embryo survival from Day 7 to 15. The solid line denotes the model fit and the dotted lines denote standard errors (P < 0.01).

      Embryo Survival for our Data (Cows with Partial Embryo Losses)

      A second analysis was based only on cows with partial embryo losses (i.e., cows with no recovered embryos were removed). Cows with complete embryo loss represent a subpopulation of cows where embryo survival is likely driven by maternal factors. An analysis of the cows with partial embryo losses represents a subpopulation where embryo factors dominate embryo survival (i.e., r = 1). For the partial embryo losses data set, there was no significant effect of Day 7 progesterone on embryo survival (βp,1 = 0.015 ± 0.015; P = 0.3) although there was a significant effect of EB from transfer to recovery on embryo survival [βEB = 0.0015 ± 0.00056 (MJ·d−1)−1; P = 0.01]. Although there was an effect of EB from 40 d before transfer on embryo survival (P = 0.05), this effect is only due to its covariance with EB from transfer to recovery. The effect of EB from transfer to recovery is independent of EB 40 d before transfer (P = 0.04). This suggests that progesterone effects on embryo survival are mediated through maternal factors, which is consistent with the observation that the effects of progesterone on bovine embryo growth are through the maternal environment (
      • Clemente M.
      • de La Fuente J.
      • Fair T.
      • Al Naib A.
      • Gutierrez-Adan A.
      • Roche J.F.
      • Rizos D.
      • Lonergan P.
      Progesterone and conceptus elongation in cattle: a direct effect on the embryo or an indirect effect via the endometrium?.
      ), whereas EB effects on embryo survival are largely mediated by direct effects on the embryo and the maternal environment.

      Trophectoderm Gene Expression

      The TE from the largest embryos recovered from each uterine tract (covering lengths from 0.34 to 170 mm) and uterine environments under a range of progesterone influence (Day 7 progesterone: 1.07–11.71 ng·mL−1) were processed for quantification by RT-PCR. The largest embryos recovered were used to represent the maximum uterine ability to stimulate growth and to reduce the effect of the variability in the size of transferred embryos (i.e., embryos between cows are more comparable). Of these, (n = 49; 4 embryos with incomplete lengths recovered were omitted) the length of the embryo correlated positively with increased expression of IFNT, TKDP1, PAG11, PTGS2, and DKK1 (r = 0.79, 0.76, 0.78, 0.63, and 0.56, respectively; P < 0.001) and correlated negatively with PDPN (r = −0.74; P < 0.001; Figure 4). No expression of DKK1 was detected in the 5 embryos 1 mm or less (a sixth produced insufficient cDNA to test for these genes). Trophectoderm longer than 19 mm (n = 31) were examined for expression of binucleate-specific genes CSH2, PRP1, and PAG9 but no expression was detected even in the longest trophectoderm (170 mm; data not shown). Embryo length was well explained by PDPN, DKK1, and PAG11 (R2 = 0.77). The effects of the remaining genes on Day 15 embryo length can be explained by their covariance with PDPN, DKK1, and PAG11.
      Figure thumbnail gr4
      Figure 4Comparison between trophectoderm (TE) length (mm) of the largest embryo recovered from each flushing of cows (n = 49, 4 fragmented TE omitted) 8 d after bulk transfer of Day 7 blastocysts and gene expression of IFNT (interferon tau); TKDP1 (trophoblast Kunitz domain protein 1); PAG11 (pregnancy-associated glycoprotein 11); PTGS2 (prostaglandin G/H synthase 2); DKK1 (dickkopf 1); and PDPN (podoplanin) measured by quantitative real-time reverse transcription-PCR. Correlation r-values are 0.79, 0.76, 0.78, 0.63, 0.56, and −0.74, respectively (P < 0.001). Data shows relative copy number of mRNA normalized against the geometric mean of the relative copy number of housekeepers GAPDH, RPL19, and UBE2K.
      Gene expression in the TE tissue of the representative embryos showed IFNT, TKDP1, PAG11, PTGS2, and DKK1 mRNA levels were positively correlated with conceptus length. Expression of trophectoderm-specific IFNT and TKDP1 is known to increase in early gestation as length increases (
      • Smith C.S.
      • Berg D.K.
      • Berg M.
      • Pfeffer P.L.
      Nuclear transfer-specific defects are not apparent during the second week of embryogenesis in cattle.
      ) as is expression of PAG11, which is most highly expressed at Day 17 of gestation and is present in both the mononucleated and binucleated cells of the trophectoderm (
      • Green J.A.
      • Xie S.
      • Quan X.
      • Bao B.
      • Gan X.
      • Mathialagan N.
      • Beckers J.F.
      • Roberts R.M.
      Pregnancy-associated bovine and ovine glycoproteins exhibit spatially and temporally distinct expression patterns during pregnancy.
      ). Another member of this large family, PAG9, is expressed exclusively in binucleate cells and has been detected in some Day 17 conceptuses (
      • Thompson I.M.
      • Cerri R.L.
      • Kim I.H.
      • Ealy A.D.
      • Hansen P.J.
      • Staples C.R.
      • Thatcher W.W.
      Effects of lactation and pregnancy on metabolic and hormonal responses and expression of selected conceptus and endometrial genes of Holstein dairy cattle.
      ). Even though several of the embryos in this trial reached a length equivalent to that of embryos previously recovered on gestational Day 17 (
      • Ledgard A.M.
      • Meier S.
      • Peterson A.J.
      Evaluation of the uterine environment early in pregnancy establishment to characterise cows with a potentially superior ability to support conceptus survival.
      ), none reached the developmental stage of TE binucleate cell formation, because mRNA for PAG9 and the other binucleate cell-specific markers CSH2 and PRP1 (
      • Patel O.V.
      • Yamada O.
      • Kizaki K.
      • Todoroki J.
      • Takahashi T.
      • Imai K.
      • Schuler L.A.
      • Hashizume K.
      Temporospatial expression of placental lactogen and prolactin-related protein-1 genes in the bovine placenta and uterus during pregnancy.
      ) was not detected. Enhanced PTGS2 expression is proposed as a blastocyst stage marker for potential pregnancy success (
      • Ghanem N.
      • Salilew-Wondim D.
      • Gad A.
      • Tesfaye D.
      • Phatsara C.
      • Tholen E.
      • Looft C.
      • Schellander K.
      • Hoelker M.
      Bovine blastocysts with developmental competence to term share similar expression of developmentally important genes although derived from different culture environments.
      ) and its positive correlation with Day 15 embryo length, as shown in the current study, suggests that it could be used as an indicator of embryonic growth. The correlation between DKK1 expression was more moderate, with no expression in the smallest, and probably undeveloped, embryos (<1 mm). We have shown here that PDPN, which is expressed in the mesothelium of secondary human yolk sac (
      • Nogales F.F.
      • Dulcey I.
      The secondary human yolk sac has an immunophenotype indicative of both hepatic and intestinal differentiation.
      ), was negatively correlated with TE length. This likely reflects the change in the proportion of mesothelial to trophectoderm cells as the conceptus elongates. It appears that TE expression of many genes is closely linked to the developmental length of the embryo.

      Embryonic Disc

      The ED of the largest embryos recovered from each uterine tract were examined by light microscopy and characterized as round, oblong, or pear-shaped (n = 25, 15, and 8 respectively; see Supplemental Figure S1; https://doi.org/10.3168/jds.2017-12845;
      • Guillomot M.
      • Turbe A.
      • Hue I.
      • Renard J.P.
      Staging of ovine embryos and expression of the T-box genes Brachyury and Eomesodermin around gastrulation.
      ). Two embryos had no ED present (TE length 0.34 and 2.6 mm) and in 2 embryos, the ED could not be found due to fragmentation of the TE. The area of the ED correlated with TE length (r = 0.77, P < 0.001; Figure 5). Length and width of the ED were highly correlated (r = 0.88, P < 0.001). Although TE growth and ED length are correlated (
      • Berg D.K.
      • van Leeuwen J.
      • Beaumont S.
      • Berg M.
      • Pfeffer P.L.
      Embryo loss in cattle between Days 7 and 16 of pregnancy.
      ) and ED developmental stages are temporally correlated with ED size (
      • van Leeuwen J.
      • Berg D.K.
      • Pfeffer P.L.
      Morphological and gene expression changes in cattle embryos from hatched blastocyst to early gastrulation stages after transfer of in vitro produced embryos.
      ), whether the ED developmental stages are equally temporally correlated is speculative. We could hypothesize that longer conceptuses have advanced ED development, although this requires further investigation.
      Figure thumbnail gr5
      Figure 5The relationship between trophectoderm lengths (log10 mm) of the largest embryo recovered from each flushing of cows 8 d after bulk transfer of Day 7 blastocysts and their embryonic disc (ED) area (log10 µm2). Correlation r-value is 0.77 (n = 45, P < 0.001).

      Effect of Progesterone, EB, and Embryo Transfer Size on the Day 15 Embryo

      Multivariate linear regression was used to investigate the effect of progesterone on Day 7, EB, and embryo transfer size on gene expression, ED size, and TE length on Day 15 embryo (this choice of predictors and response variables satisfies temporal causality). Because gene expression, ED size, and TE length on Day 15 were highly correlated, multivariate analysis (Eq. [13]) can be used to assess the variables simultaneously and determine the key elements that produced them (
      • Rencher A.C.
      Methods of Multivariate Analysis.
      ). The multivariate regression parameter coefficient estimates are listed in Table 2, and the correlation matrix for the error variance-covariance matrix is given in Table 3. We detected a significant effect of Day 7 progesterone on the expression of all 6 genes, ED size, and TE length on Day 15. This effect was independent of the estimated covariance between the observations on Day 15 (Table 3), suggesting that progesterone acts through multiple pathways to modify these Day 15 observations. In particular, there was a significant effect of progesterone on ED area independent of the effect of progesterone on TE length (i.e., the effect of progesterone on ED area was not due to the covariance between ED area and TE length). Furthermore, progesterone affected gene expression independently of the progesterone effect on TE length. We also detected significant effects of embryo transfer size on TE length and expression of IFNT and PAG11. This highlights that IFNT is not solely dependent on TE length. Effects of embryo transfer size on other genes operate through covariance with these response variables. Energy balance from transfer to recovery had significant effects on PDPN (P < 0.01), TKDP1 (P < 0.05), and TE length (P < 0.01). This provides candidate signaling pathways for the effect of EB on embryo growth to Day 15.
      Table 2The multivariate regression parameter coefficient estimates for the effect of progesterone on Day 7 (ng/mL), embryo transfer size (log10 cells), and energy balance from transfer to recovery (MJ/d) on gene expression,
      Gene expression is expressed as log10 (relative copy number × 103).
      embryonic disc area (ED; log10 μm2), and trophectoderm length (TL; log10 mm) of Day 15 embryos
      ItemIFNTTKDP1PDPNPTGS2DKK1PAG11EDTL
      Intercept−1.69 ± 2.30−0.74 ± 2.286.31 ± 3.21
      P < 0.05
      −4.83 ± 3.84−3.89 ± 2.72−4.33 ± 3.371.16 ± 2.75−10.6 ± 4.10
      P < 0.01
      Progesterone Day 70.055 ± 0.016
      P < 0.001.
      0.054 ± 0.016
      P < 0.001.
      −0.079 ± 0.023
      P < 0.001.
      0.084 ± 0.027
      P < 0.01
      0.069 ± 0.019
      P < 0.001.
      0.053 ± 0.024
      P < 0.05
      0.059 ± 0.020
      P < 0.01
      0.15 ± 0.028
      P < 0.001.
      Embryo transfer size2.31 ± 1.05
      P < 0.05
      1.61 ± 1.04−1.92 ± 1.462.78 ± 1.752.07 ± 1.24
      P < 0.10
      3.35 ± 1.54
      P < 0.05
      1.51 ± 1.255.05 ± 1.87
      P < 0.01
      Energy balance0.0013 ± 0.00080.0017 ± 0.0008
      P < 0.05
      −0.0033 ± 0.0010
      P < 0.01
      0.00084 ± 0.0013−0.00048 ± 0.000900.0015 ± 0.00120.00061 ± 0.000890.0045 ± 0.0014
      P < 0.01
      1 Gene expression is expressed as log10 (relative copy number × 103).
      P < 0.10
      * P < 0.05
      ** P < 0.01
      *** P < 0.001.
      Table 3Correlation matrix (variances in parentheses) for the estimated error variance-covariance matrix from the multivariate regression of the effect of progesterone on Day 7 (ng/mL), energy balance from transfer to recovery (MJ/d), and embryo transfer size (log10 cells) on gene expression,
      Gene expression is expressed as log10 (relative copy number × 103).
      embryonic disc area (ED; log10 μm2), and trophectoderm length (TL; log10 mm) of Day 15 embryos.
      GeneIFNTTKDP1PDPNPTGS2DKK1PAG11EDTL
      IFNT1.00 (0.10)0.88−0.420.540.630.760.570.72
      TKDP11.00 (0.10)−0.510.720.470.670.520.67
      PDPN1.00 (0.18)−0.60−0.30−0.38−0.57−0.61
      PTGS21.00 (0.26)0.320.490.510.54
      DKK11.00 (0.12)0.460.590.57
      PAG111.00 (0.21)0.560.77
      ED area1.00 (0.12)0.70
      TL1.00 (0.32)
      1 Gene expression is expressed as log10 (relative copy number × 103).
      Although IFNT expression was detectable in Day 8 blastocysts (
      • Watson A.J.
      • Hogan A.
      • Hahnel A.
      • Wiemer K.E.
      • Schultz G.A.
      Expression of growth factor ligand and receptor genes in the preimplantation bovine embryo.
      ), modeling of the embryo–uterine biological interactions indicates that a time-dependent minimal amount of IFNT protein must be present in the luminal fluid to ensure pregnancy recognition (
      • Shorten P.R.
      • Peterson A.J.
      • O'Connell A.R.
      • Juengel J.L.
      • McNatty K.P.
      • Soboleva T.K.
      A mathematical model of pregnancy recognition in mammals.
      ). This amount, correlated with embryo length, needs to be determined at the crucial window of IFNT influence. An indication of a threshold has been reported, measured as a difference in IFNT-responsive genes of the peripheral blood mononuclear cells between cows receiving a uterine infusion of recombinant IFNT at 500 compared with 1,000 µg·kg−1 of BW (
      • Matsuyama S.
      • Kojima T.
      • Kato S.
      • Kimura K.
      Relationship between quantity of IFNT estimated by IFN-stimulated gene expression in peripheral blood mononuclear cells and bovine embryonic mortality after AI or ET.
      ).

      Role of Gene Expression on Embryo Survival to Day 15

      We detected significant independent effects of TKDP1, PAG11, and PDPN on embryo survival: βTKDP1 = −0.39 ± 0.15 [log10 (RCN × 103)]−1, P = 0.01; βPAG11 = 0.36 ± 0.10 [log10 (RCN × 103)]−1, P = 0.01; and βPDPN = −0.16 ± 0.08 [log10 (RCN × 103)]−1, P = 0.04, Eq. [10]. However, we found no significant effect of EB from transfer to recovery on embryo survival from transfer to recovery when effects due to TKDP1, PAG11, and PDPN were accounted for in the model (P = 0.3). This suggests that effects of EB on embryo survival in cows with partial embryo losses are largely mediated via TKDP1, PAG11, and PDPN. This also provides candidate signaling pathways for the effect of EB on embryo growth to Day 15.

      CONCLUSIONS

      In the current study, bulk transfer of Day 7 IVP blastocysts resulted in embryos with considerable variation in length recovered 8 d later, even from the same uterine environment. Mathematical models of embryo survival allowed both uterine receptiveness and embryo quality factors on embryo survival to be described and allowed these dual components of the biology to be analyzed. The EG model presented here was validated using literature data and experimental data from this trial and provides a description of the complex interaction between progesterone and blastocyst developmental stage on embryo growth. The model provided good predictions of progesterone on days where progesterone was not measured. We used the model to estimate the time delay (4.75 ± 0.16 d) between an increase in circulating progesterone and an increase in uterine competence. We also found that doubling progesterone increased the embryo growth rate by around 33%. The EG model captured the main features of embryo growth kinetics because it was able to predict the effect of progesterone and developmental stage on embryo growth for both literature data and our data, demonstrating its utility. Others have shown a clear relationship between the kinetics of development of early bovine embryos to first cleavage after insemination and developmental competence. However, we found that although Day 15 embryo size depends on the specific morphological stage (indicative of cell number or size) of the Day 7 blastocyst when it was transferred, progesterone is a more important factor than transferred embryo size on subsequent growth.

      ACKNOWLEDGMENTS

      We thank P. Sharpe (ET services, Hamilton, New Zealand) for sample collection; staff of AgResearch (Ruakura, Hamilton, New Zealand); staff of Tokanui Farm for animal husbandry; S. Delaney and C. Smith (AgResearch) for sample collection; S. Franke for technical assistance; and P. Hunt (AgResearch) for graphic arts. This work was supported by AgResearch Core funding.

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