Estimation of Glucose Uptake by Ovarian Follicular Cells

Abstract

In vitro maturation (IVM) of mammalian oocytes provides an alternative to traditional in vitro fertilization techniques for clinical treatment of infertility or animal breeding. IVM involves the collection of oocytes from the ovary prior to ovulation, with maturation occurring in a laboratory environment. The success of IVM is highly sensitive to the in vitro nutrient environment. The nurse cells surrounding the oocyte, known as cumulus cells, regulate this environment and removal of these cells reduces the ability of the oocyte to develop following insemination. Determining the nature of the interaction between the oocyte and cumulus cells, collectively called the cumulus–oocyte complex (COC), is a difficult task experimentally. Here we use a combination of experimental and mathematical techniques to investigate glucose transport within bovine COCs and find quantitative estimates of the glucose uptake rates of the oocyte and cumulus cells. Surprisingly, our modeling shows the rate of uptake of glucose by the oocyte to increase and then decrease with concentration, a result that needs further experimental investigation but which supports the expectation that high and low glucose concentrations are detrimental to oocyte development. The methodology described is suitable for use across species and for investigating the transport of other important nutrients within the COC.

Appendices

Appendix A

If glucose uptake is described by a Michaelis–Menten function it takes the form

$$ \frac{{V_{\max } C}}{{K_{\text{m}} + C}}, $$

where C is glucose concentration and V _max and K _m are Michaelis–Menten parameters. The Michaelis–Menten function has proved to be an adequate description of carrier facilitated transport uptake in several cell types,20 and glucose carrier proteins are often characterized by a Michaelis–Menten parameter (their K _M value).17 Therefore, a Michaelis–Menten form for glucose uptake in COCs or granulosa cells is assumed appropriate. As measured glucose concentrations were of the form C(t) we use the integrated form of the Michaelis–Menten equation (the Schnell–Mendoza equation28)

$$ C(t) = K_{\text{m}} W\left( {\frac{{C_{0} }}{{K_{\text{m}} }}\exp \left( {\frac{{ - V_{\max } t + C_{0} }}{{K_{\text{m}} }}} \right)} \right), $$

(A.1)

where C ₀ is the glucose concentration at t = 0 and W(x) is the omega function

$$ W(x)\exp (W(x)) = x. $$

(A.2)

MATLAB’s Symbolic Math Toolbox was used to evaluate values of the omega function (MATLAB 7.0.1, The MathWorks Inc., 2004).

The Michaelis–Menten function has two limiting cases. The first is when uptake is proportional to concentration, yielding

$$ C(t) = C_{0} \exp \left( {\frac{{ - V_{\max } t}}{{K_{\text{m}} }}} \right) = C_{0} \exp \left( { - At} \right), $$

(A.3)

and the second is when uptake is a constant, yielding

$$ C(t) = C_{0} - V_{\max } t. $$

(A.4)

These two limiting cases were also considered as possible simpler models of glucose uptake by granulosa cells or COCs.

Each data point consists of a measured concentration, C(t), the time of measurement, t, and the initial glucose concentration in that sample, C ₀. Equation (A.1) was fitted to the data to obtain the constants V _max and K _m via a weighted non-linear regression using the Gauss–Newton Method with varying step size.27 In this method a surface representing the weighted sum

$$ S(t) = \sum\limits_{i = 1}^{n} {W_{i} (c_{i} - C_{i} )^{2} } , $$

(A.5)

is minimized, where W _i  = 1/C ² _i are weight functions, c _i is an experimental data point, and C _i is the predicted value of concentration at the time corresponding to the data point c _i . The form chosen here was used because the biological data considered here has constant percentage errors (COBAS machine measurement error is a percentage of measured concentration).29

To illustrate fit properties, the percentage residual between the fit and each data point are plotted in Fig. 7. In addition 95% confidence regions for each fit are also shown. These confidence regions are obtained by plotting the contours of S(t) when

$$ S(t) = S(\hat{t})\left[ {1 + \frac{k}{n - k}F(k,n - k,\alpha )} \right], $$

(A.6)

where $S(\hat{t})$ is the minimum value of S(t) calculated using (A.5), F(k,n − k,α) is the critical value of the F-distribution at the (1 − α) significance level, k is the number of model parameters and n is the number of data points.1

Figure 7

Predicted concentration values plotted against the fit residuals for (a) granulosa cells and (b) COCs. The crosses show best fits to data. Also shown are 95% confidence regions for fit parameters for (c) granulosa cells and (d) COCs

The confidence region for granulosa cells appears to be large. This suggests that the relationship between glucose uptake and concentration in granulosa cells may be adequately described as being proportional to concentration (as in (A.3))1; however, a comparison between Michaelis–Menten and linear fits using the F-ratio test1 suggested that the Michaelis–Menten fit was more appropriate to these data at the 95% level (p = 0.045 for granulosa cells and p < 0.01 for COCs). For both granulosa cells and COCs the Michaelis–Menten fit to data was found to be more appropriate than the assumption of constant uptake at the 99% level (p < 0.01 in each case).

Appendix B

Oocyte handling medium (OHM) is comprised of the components in Table 4. For the purpose of the experimentation described here, OHM is made up glucose free and then glucose is added to make stocks of appropriate concentrations. All chemicals were purchased from Sigma, St. Louis, USA. MEM amino acids were purchased in liquid form. Standard osmolality and pH for OHM are 7.2–7.3 and 270–280 mOsm, respectively.

Table 4 Composition of oocyte handling medium (OHM)