Register      Login
Reproduction, Fertility and Development Reproduction, Fertility and Development Society
Vertebrate reproductive science and technology
RESEARCH ARTICLE

Numerical calculations for diffusion effects in the well-of-the-well culture system for mammalian embryos

Koji Matsuura
+ Author Affiliations
- Author Affiliations

Research Core for Interdisciplinary Sciences, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530, Japan. Email: kojimatu@md.okayama-u.ac.jp

Reproduction, Fertility and Development 26(5) 742-751 https://doi.org/10.1071/RD13025
Submitted: 28 January 2013  Accepted: 1 May 2013   Published: 23 May 2013

Abstract

Recent studies suggest that the microenvironment and embryo density used during embryo culture considerably affect development to the blastocyst stage. High embryo density allows for autocrine secretions to diffuse to neighbouring embryos during group culture, with a positive effect on further development. A variation of group culture is the well-of-the-well (WOW) culture system, allowing for individual identification of embryos cultured in small holes in a microdroplet. Bovine blastocyst development is higher in the WOW culture system than in conventional group culture. To compare the concentration of chemical factors between conventional and WOW culture, a model was constructed to calculate the concentration of secreted factors based on Fick’s second law of diffusion using spreadsheet software. Furthermore, model was used to determine the concentration of growth factors and waste materials adjacent to the embryo periphery. The results of these calculations suggest that the highest difference in the concentration of secreted small molecules and macromolecules was at the most two- to threefold, with the concentrations reduced more and diffusion kinetics facilitated to a greater extent in the WOW culture system. The average ratio of the concentration of secreted macromolecules (10 nm diameter) around the embryos was also compared between systems with well widths of 0.1 and 0.3 mm. The concentration of secreted materials surrounding embryos increased in a narrow tapered well. The findings suggest that the WOW culture system is better than conventional group culture because of the increased final concentration of autocrine factors and higher diffusion kinetics of waste materials.

Additional keywords: autocrine effect, in vitro embryo culture.


References

Akagi, S., Hosoe, M., Matsukawa, K., Ichikawa, A., Tanikawa, T., and Takahashi, S. (2010). Culture of bovine embryos on a polydimethylsiloxane (PDMS) microwell plate. J. Reprod. Dev. 56, 475–479.
Culture of bovine embryos on a polydimethylsiloxane (PDMS) microwell plate.Crossref | GoogleScholarGoogle Scholar | 20484872PubMed |

Ali, A. A., Bilodeau, J. F., and Sirard, M. A. (2003). Antioxidant requirements for bovine oocytes varies during in vitro maturation, fertilization and development. Theriogenology 59, 939–949.
Antioxidant requirements for bovine oocytes varies during in vitro maturation, fertilization and development.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3sXotVSh&md5=153632ccd4cdfa3deaa02cb88a414ff8CAS | 12517395PubMed |

Crank, J. (1975). ‘The mathematics of diffusion’, 2nd edn. (Clarendon Press: Oxford.)

Domínguez, F., Gadea, B., Esteban, F. J., Horcajadas, J. A., Pellicer, A., and Simón, C. (2008). Comparative protein-profile analysis of implanted versus non-implanted human blastocysts. Hum. Reprod. 23, 1993–2000.
Comparative protein-profile analysis of implanted versus non-implanted human blastocysts.Crossref | GoogleScholarGoogle Scholar | 18556682PubMed |

Ebner, T., Shebl, O., Moser, M., Mayer, R. B., Arzt, W., and Tews, G. (2010). Group culture of human zygotes is superior to individual culture in terms of blastulation, implantation and life birth. Reprod. Biomed. Online 21, 762–768.
Group culture of human zygotes is superior to individual culture in terms of blastulation, implantation and life birth.Crossref | GoogleScholarGoogle Scholar | 1:STN:280:DC%2BC3cbpvFKisg%3D%3D&md5=38b372e46dd2ec0d9b0000fd8fd46d9bCAS | 21051291PubMed |

Gopichandran, N., and Leese, H. J. (2006). The effect of paracrine/autocrine interactions on the in vitro culture of bovine preimplantation embryos. Reproduction 131, 269–277.
The effect of paracrine/autocrine interactions on the in vitro culture of bovine preimplantation embryos.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD28XisFalsL0%3D&md5=8dc227773630ac7b080a72a7da882ac8CAS | 16452720PubMed |

Hardy, K., and Spanos, S. (2002). Growth factor expression and function in the human and mouse preimplantation embryo. J. Endocrinol. 172, 221–236.
Growth factor expression and function in the human and mouse preimplantation embryo.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD38XhvVejt78%3D&md5=eb91d6393ace8689e9af65446fc5cc36CAS | 11834440PubMed |

Hashimoto, S., Kato, N., Saeki, K., and Morimoto, Y. (2012). Selection of high-potential embryos by culture in poly(dimethylsiloxane) microwells and time-lapse imaging. Fertil. Steril. 97, 332–337.
Selection of high-potential embryos by culture in poly(dimethylsiloxane) microwells and time-lapse imaging.Crossref | GoogleScholarGoogle Scholar | 22217963PubMed |

Heo, Y. S., Cabrera, L. M., Bormann, C. L., Smith, G. D., and Takayama, S. (2012). Real time culture and analysis of embryo metabolism using a microfluidic device with deformation based actuation. Lab Chip 12, 2240–2246.
Real time culture and analysis of embryo metabolism using a microfluidic device with deformation based actuation.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC38XnsFOmsro%3D&md5=0c37e6fd51d90820c4420e4a67c2946cCAS | 22402469PubMed |

Hizuka, N., Fukuda, I., Takano, K., Asakawa-Yasumoto, K., Okubo, Y., and Demura, H. (1998). Serum high molecular weight form of insulin-like growth factor II from patients with non-islet cell tumor hypoglycemia is O-glycosylated. J. Clin. Endocrinol. Metab. 83, 2875–2877.
Serum high molecular weight form of insulin-like growth factor II from patients with non-islet cell tumor hypoglycemia is O-glycosylated.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK1cXltlWrurw%3D&md5=fe094982007590371fa8cb62042560b9CAS | 9709962PubMed |

Hoelker, M., Rings, F., Lund, Q., Ghanem, N., Phatsara, C., Griese, J., Schellander, K., and Tesfaye, D. (2009). Effect of the microenvironment and embryo density on developmental characteristics and gene expression profile of bovine preimplantative embryos cultured in vitro. Reproduction 137, 415–425.
Effect of the microenvironment and embryo density on developmental characteristics and gene expression profile of bovine preimplantative embryos cultured in vitro.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1MXovV2ksbg%3D&md5=2d294fb6e32540127c3be7a5560d4fd2CAS | 19098140PubMed |

Iwai, Y., Oomura, T., Koito, Y., Kobayashi, K., Tomimura, M., Haneda, M., Hirasawa, S., and Yoshida, H. (2010). ‘Numerical Simulation of Thermal Fluids Using Excel Spread Sheet and a Mouse.’ (Maruzen: Tokyo.) [In Japanese]

Katz-Jaffe, M. G., Schoolcraft, W. B., and Gardner, D. K. (2006). Analysis of protein expression (secretome) by human and mouse preimplantation embryos. Fertil. Steril. 86, 678–685.
Analysis of protein expression (secretome) by human and mouse preimplantation embryos.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD28XhtFCqsL%2FO&md5=2ffce80df7db56b2be8a519d11792332CAS | 16952510PubMed |

Kawamura, K., Chen, Y., Shu, Y., Cheng, Y., Qiao, J., Behr, B., Pera, R. A. R., and Hsueh, A. J. W. (2012). Promotion of human early embryonic development and blastocyst outgrowth in vitro using autocrine/paracrine growth factors. PLoS One 7, e49328.
Promotion of human early embryonic development and blastocyst outgrowth in vitro using autocrine/paracrine growth factors.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC38XhslCqu7fF&md5=42b459492c74d64f714c3e4867644382CAS | 23152897PubMed |

Lane, M., and Gardner, D. K. (2003). Ammonium induces aberrant blastocyst differentiation, metabolism, pH regulation, gene expression and subsequently alters fetal development in the mouse. Biol. Reprod. 69, 1109–1117.
Ammonium induces aberrant blastocyst differentiation, metabolism, pH regulation, gene expression and subsequently alters fetal development in the mouse.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3sXnsV2nsr8%3D&md5=c3fe97f4803900194393a252aeb6c33bCAS | 12773416PubMed |

Luetteke, N. C., Michalopoulos, G. K., Teixido, J., Gilmore, R., Massague, J., and Lee, D. C. (1988). Characterization of high molecular weight transforming growth factor alpha produced by rat hepatocellular carcinoma cells. Biochemistry 27, 6487–6494.
Characterization of high molecular weight transforming growth factor alpha produced by rat hepatocellular carcinoma cells.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaL1cXkvFSmsLc%3D&md5=f577a9017309408f99e38540fe4863e0CAS | 3219349PubMed |

Nagao, Y., Iijima, R., and Saeki, K. (2008). Interaction between embryos and culture conditions during in vitro development of bovine early embryos. Zygote 16, 127–133.
Interaction between embryos and culture conditions during in vitro development of bovine early embryos.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1cXksF2mur8%3D&md5=5f48387266c8a5a84db7f47b1bdb2ba8CAS | 18405433PubMed |

Neira, J. A., Tainturier, D., Penã, M. A., and Martal, J. (2010). Effect of the association of IGF-I, IGF-II, bFGF, TGF-b1, GM-CSF, and LIF on the development of bovine embryos produced in vitro. Theriogenology 73, 595–604.
Effect of the association of IGF-I, IGF-II, bFGF, TGF-b1, GM-CSF, and LIF on the development of bovine embryos produced in vitro.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC3cXitVOiurk%3D&md5=911621fdfabf6362ea4d4c1940089d7cCAS | 20035987PubMed |

O’Neill, C. (2008). The potential roles for embryotrophic ligands in preimplantation embryo development. Hum. Reprod. Update 14, 275–288.
The potential roles for embryotrophic ligands in preimplantation embryo development.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1cXkvFOqtbw%3D&md5=9760bd28fe35aa89442a0e656bef9774CAS | 18281694PubMed |

Palladino, M. A., Bahjat, F. R., Theodorakis, E. A., and Moldawer, L. L. (2003). Anti-TNF-α therapies: the next generation. Nat. Rev. Drug Discov. 2, 736–746.
Anti-TNF-α therapies: the next generation.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3sXmvVWlsLc%3D&md5=0586f58c9879e94029d70c2410f4a362CAS | 12951580PubMed |

Rinderknecht, E., and Humbel, R. E. (1978). The amino acid sequence of human insulin-like growth factor I and its structural homology with proinsulin. J. Biol. Chem. 253, 2769–2776.
| 1:CAS:528:DyaE1cXktlyhu7s%3D&md5=9950af10140d80be288beb94bd0df83dCAS | 632300PubMed |

Rodina, T. M., Cooke, F. N. T., Hansen, P. J., and Ealy, A. D. (2009). Oxygen tension and medium type actions on blastocyst development and interferon-tau secretion in cattle. Anim. Reprod. Sci. 111, 173–188.
Oxygen tension and medium type actions on blastocyst development and interferon-tau secretion in cattle.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1MXhsFKmtrk%3D&md5=7ea0c14bdea1d0d745a4c2091afe7331CAS | 18394828PubMed |

Seksek, O., Biwersi, J., and Verkman, A. S. (1997). Translational diffusion of macromolecule-sized solutes in cytoplasm and nucleus. J. Cell Biol. 138, 131–142.
Translational diffusion of macromolecule-sized solutes in cytoplasm and nucleus.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DyaK2sXksF2hurg%3D&md5=8cc54c4c9432fc15b9bc35d204639bfbCAS | 9214387PubMed |

Seli, E., Robert, C., and Sirard, M. A. (2010). OMICS in assisted reproduction: possibilities and pitfalls. Mol. Hum. Reprod. 16, 513–530.
OMICS in assisted reproduction: possibilities and pitfalls.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC3cXptlegt7k%3D&md5=5cf278d1121a052324cde86e665b3333CAS | 20538894PubMed |

Smith, G. D., Takayama, S., and Swain, J. E. (2012). In vitro embryo culture: new developments in culture platforms and potential to improve assisted reproductive technologies. Biol. Reprod. 86, 62.
| 21998170PubMed |

Stokes, P. J., Abeydeera, L. R., and Leese, H. J. (2005). Development of porcine embryos in vivo and in vitro; evidence for embryo ‘cross talk’ in vitro. Dev. Biol. 284, 62–71.
Development of porcine embryos in vivo and in vitro; evidence for embryo ‘cross talk’ in vitro.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD2MXntVGns7Y%3D&md5=b15f74b5bb7b2e11e9c8b6a22af8f56cCAS | 15963973PubMed |

Sugimura, S., Akai, T., Somfai, T., Hirayama, M., Aikawa, Y., Ohtake, M., Hattori, H., Kobayashi, S., Hashiyada, Y., Konishi, K., and Imai, K. (2010). Time-lapse cinematography-compatible polystyrene-based microwell culture system: a novel tool for tracking the development of individual bovine embryos. Biol. Reprod. 83, 970–978.
Time-lapse cinematography-compatible polystyrene-based microwell culture system: a novel tool for tracking the development of individual bovine embryos.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC3cXhsFahu77I&md5=f832d61a7b82c1524bdce6fba40c34f4CAS | 20739661PubMed |

Taka, M., Iwayama, H., and Fukui, Y. (2005). Effect of the well of the well (WOW) system on in vitro culture for porcine embryos after intracytoplasmic sperm injection. J. Reprod. Dev. 51, 533–537.
Effect of the well of the well (WOW) system on in vitro culture for porcine embryos after intracytoplasmic sperm injection.Crossref | GoogleScholarGoogle Scholar | 16141648PubMed |

Vajta, G., Peura, T. T., Holm, P., Paldi, A., Greve, T., Trounson, A. O., and Callesen, H. (2000). New method for culture of zona-included or zona-free embryos: the well of the well (WOW) system. Mol. Reprod. Dev. 55, 256–264.
New method for culture of zona-included or zona-free embryos: the well of the well (WOW) system.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3cXhtFelsbY%3D&md5=89231e118949efd9f1972f7bcc1e0795CAS | 10657044PubMed |

Venturoli, D., and Rippe, B. (2005). Ficoll and dextran vs. globular proteins as probes for testing glomerular permselectivity: effects of molecular size, shape, charge, and deformability. Am. J. Physiol. Renal Physiol. 288, F605–F613.
Ficoll and dextran vs. globular proteins as probes for testing glomerular permselectivity: effects of molecular size, shape, charge, and deformability.Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD2MXjtlOqtr0%3D&md5=d783e108cd03df3bbc56c3b62fb6b6d7CAS | 15753324PubMed |