Introduction
Diabetic pregnancies are associated with maternal type 2 diabetes (T2D) after delivery as well as T2D, metabolic syndrome, and atherosclerotic diseases in their offspring early in life. Reference Guariguata, Linnenkamp, Beagley, Whiting and Cho1–Reference Eberle and Ament3 The global prevalence of hyperglycemia in pregnancy (HIP) was 15.8% of live births to women in 2019 referring to the International Diabetes Federation (IDF) 2 – with an upward trend and an increased estimated number of unreported cases. HIP comprises pregestational diabetes in pregnancy, which may play a role in approximately 7.9% of HIP cases, other types of diabetes first detected in pregnancy in approximately 8.5% of HIP cases as well as gestational diabetes mellitus (GDM), which affect approximately 83.6% of HIP cases. 2 The HIP prevalence varies in different IDF world regions between 7.5% and 27.0%, 2 depending on risk factors like maternal age, body mass index, diabetic history as well as ethnic, social, and income groups. Reference Guariguata, Linnenkamp, Beagley, Whiting and Cho1,Reference Eberle and Ament3 Many authors postulate that maternal diabetes accompanied by obesity seems to be the main driving metabolic programming issue in terms of dysmetabolic conditions in their offspring. In contrast, our data will clearly indicate that maternal diabetes per se (without accompanied obesity) seems to be a strong risk or imprinting factor in terms of diabetic programming leading to diabetes as well as metabolic and cardiovascular diseases in the offspring early in life.
Since it is not explicitly known how maternal diabetic in utero environment imprints the fetus for diabetes and metabolic syndrome as well as atherosclerotic disease later in life, we analyzed the Ins2 Akita mouse model, in which the offspring of diabetic mothers (DMs) develop diabetes, accompanied by altered insulin sensitivities as well as abnormal glucose-stimulated insulin release.
Focusing on epigenetic or other aspects, multiple mechanisms of in utero and perinatal programming may play a key role. “Perinatal programming” defines the perturbation at one or more critical periods during development causing persistent alterations with sometimes irreversible consequences. Reference Eberle and Ament3 To characterize and assess mechanisms of diabetic programming, appropriate predictors as well as therapeutic approaches have to be found.
We have recently proposed a newly established dynamic in silico model and have shown that parameter identification provides individual predictors characterizing different types of metabolic diseases already at an early stage. Reference Eberle, Palinski and Ament4,Reference Eberle, Niessen, Hemmings, Tschopp and Ament5 We showed that model parameters such as short-term and long-term glucose sensitivities, k G1 and k G2, respectively, are suitable for significantly predicting metabolic developments at early stages for subjects within one generation.
In this contribution, we will extend this approach by targeting trans-generational diabetic in utero programming. We have to identify specific individual predictors, such as k G1 and k G2, for diabetic development in offspring and analyze their relationship to maternal diabetic imprinting.
We will show that in silico model-based predictors are an effective approach to obtain significant results even in the case of small-group sizes, including high sensitivity as well as high specificity.
Method
In vivo model
The Ins2 Akita mouse model presents an established diabetic model with appealing characteristics, such as altered insulin sensitivity as well as abnormal glucose-stimulated insulin release.
Due to a misfolded insulin-2 protein, which causes endoplasmic reticulum stress and β-cell death, insulin processing is disrupted, which results in the early development of hyperglycemia. Additionally, by using Ins2 Akita mice, the mechanisms of type 2 diabetes could be investigated without the associated interference of obesity.
Within the experimental setup shown in Fig. 1, a group of DMs is established based on the C57BL/6-J-Ins2 Akita mouse model. They are compared to matched C57BL/6-J mice, which are denoted as nondiabetic mothers (NDMs). Both groups have equivalent conditions prior to and during pregnancy. Body weight and plasma glucose levels are controlled on a daily basis during pregnancy. There are no relevant differences in body weight, neither pre-conceptional nor during the first 13 days of pregnancy. However, in the final stage of pregnancy, the gestational weight gain of NDM is higher than that of DM (NDM 39.0 ± 3.0 g vs. DM 31.6 ± 2.4 g at day 19 of pregnancy, denoting mean ± standard deviation). As expected, the fasting plasma glucose levels in DM are raised compared to NDM during the whole period of pregnancy (NDM 151.6 ± 17.5 mg/dl vs. DM 179.7 ± 23.9 mg/dl, denoting mean ± standard deviation).
Fig. 1. Setup of the in vivo experiment. Offspring were assigned by polymerase chain reaction to negative control (black), experimental (red), and positive control (blue) groups; in addition, offspring were classified and matched by age as well as sex into groups (A) to (M), and the number of subjects in each group is denoted with n.
This study focuses on specific trans-generational diabetic programming aspects, which are defined as not directly genetically determined impacts from mothers to their offspring. Hence, the offspring of DMs who were not genetically determined to diabetes (wild type; wt C57BL/6-J-Ins2 Akita ) are classified as the experimental group. They are compared to the offspring of NDMs who are neither genetically determined nor affected by diabetic programming (C57BL/6-J as a negative control group). To allow a comparison to genetically moderated mechanisms, a positive control group of genetically determined offspring (C57BL/6-J-Ins2 Akita ) of DM is also considered. Fig. 1 gives a survey of the three resulting offspring groups.
All offspring were raised under equivalent experimental conditions. Their body weights and fasting glucose concentrations were measured regularly. At 3 and 11 weeks of age, an intraperitoneal glucose tolerance test (IPGTT) was performed for all offspring. The experimental setup and the definition of the groups (A) to (M) for female and male offspring at 3 and 11 weeks of age, including their sizes n, are summarized in Fig. 1.
In silico model
In silico models can be used to simulate and characterize dynamical processes, for example, glucose insulin dynamics during an IPGTT. A survey of appropriate models in diabetes is given by Cobelli et al.
Reference Cobelli, Dalla Man, Sparacino, Magni, De Nicolao and Kovatchev6
To provide an appropriate in silico model, we redefined Bergman’s “minimal model”
Reference Bergman, Ider, Bowden and Cobelli7,Reference Bergman, Phillips and Cobelli8
as developed in Eberle et al.
Reference Eberle, Palinski and Ament4
The block diagram of the resulting nonlinear model is displayed in Fig. 2 within the green panel using transfer functions (shown as white blocks). It comprises the functional compartments of the plasma, interstitial tissue, pancreatic controller, and external inputs. All components can be assigned to either the glucose subsystem (upper part) or the insulin subsystem (lower part). Two external inputs, an intraperitoneal glucose bolus u
GP
and an intraperitoneal insulin bolus u
IP
, are provided. To simulate an IPGTT, an impulse function at t = 0 min is applied to u
GP
, whereas u
IP
remains zero. The simulated plasma glucose concentration
$\hat{G} $
serves as model output (Fig. 2).
Fig. 2. Block diagram of the in silico model comprising functional compartments of the plasma, interstitial tissue, pancreatic control, intraperitoneal tissue, and external inputs (in green). Simulated glucose values
$\hat{G} $
are compared to measured values G from the in vivo model (in blue). For identification, a cost function J is minimized (gray box) with respect to the in silico model parameters p (in red). Finally, they serve as predictors.
Identification of in silico model-based predictors
In the approach presented here, the measured IPGTT data retrieved from the in vivo model are used for the identification of individual in silico models. For each subject, the measured plasma glucose values G are compared with the simulated glucose values
$\hat{G} $
(see Fig. 2). A cost function J is defined to assess their deviations:
$$J(\;p): = \sum\limits_{k = 1}^N {{{\left[ {\hat{G} (k,p) - G(k)} \right]}^2} + 10{\mkern 1mu} {{\left[ {p - {p_0}} \right]}^2}} .$$
In the first term, the squared differences between G and
$\hat{G} $
are summed over the N = 7 measurements during an IPGTT at time steps t = 0, 15, 30, 45, 60, 90, and 120 min. The second term considers the squared difference of the current parameter vector
p
to its initial definition
p
0. In
p
, the four most relevant in silico model parameters
$$p = {\left[ {{G_{{\rm{basal}}}},\;{k_G}_1,\;{k_G}_2,\;{k_{GP}}} \right]^T}$$
are selected. They are printed in red in the in silico model block diagram of Fig. 2. We proved the identifiability of this set of parameters p according to. Reference Eberle and Ament9,Reference Eberle and Ament10 For diagnostic purposes, we will use the first three parameters:
-
the basal plasma glucose G basal;
-
the first-phase (short term) glucose response gain k G1; and
-
the second-phase (long term) glucose response gain k G2.
The fourth parameter, the gain of the intraperitoneal glucose dosage k GP, only serves as an auxiliary parameter for model adjustment, which will improve identification accordance.
For each subject, a simplex optimization algorithm Reference Nelder and Mead11 implemented in MATLAB© is applied to solve the optimization problem by minimizing the cost function J and to fit the in silico model to the subject’s measurement in the best possible way.
Finally, an optimized p is available for each subject, providing in silico model-based predictors (Fig. 2) for the two subsequent analysis procedures.
Pooled predictors and their effects
How specific are the in silico model-based predictors retrieved only from offspring when they are applied to forecast maternal imprinting? Statistical measures can be applied. To assess the impact of a feature difference between groups, we suggest its effect e, which is defined as the mean
${\overline y _2}$
of a subset of subjects holding this feature compared with the mean
${\overline y _1}$
of a subset comprising subjects without the feature:
$$e = {\overline y _2} - {\overline y _1}.$$
This measure is commonly used in the design of experiments field.
Reference Montgomery12
For example, to calculate the effect of the offspring sex at 11 weeks of age,
${\overline y _2}$
is calculated from the mean of all female groups (K), (L), (M) with n = 22, and
${\overline y _1}$
is calculated from all male groups (G), (H), and (I) with n = 23. In this way, larger group sizes n are achieved, and a double-sided t-test can be applied to determine the level of significance P
e
of the corresponding effect e.
Classification of individual predictors
A classification of individual predictors may serve as an alternative method that does not require static methods and, therefore, is independent of certain group sizes that are necessary for significance. We use, for example, the n = 45 data sets at 11 weeks of age (all subjects included in groups (G) to (M)) to train a classification tree. Reference Coppersmith, Hong and Hosking13 Each data set comprises the predictors {G basal, k G1, k G2} and the known maternal class. The training was performed with the Statistics and Machine Learning Toolbox of MATLAB©.
Thereafter, classification success can be presented as confusion matrix C, which counts all N data sets referring to the known classes assigned as rows and to the predicted classes assigned as columns. Correct classifications are counted as main diagonal elements, and their share of all data sets is
$${P_c} = {\rm{trace}}(C)/n.$$
Results
In vivo model
The plasma glucose development G(t) during IPGTT shows a positive deflection as a response to the intraperitoneal glucose administration at t = 0 min in all cases. At 3 weeks of age (Fig. 3), a high maximum amplitude of approximately 400 mg/dl at t = 15 min and a complete remission to basal values at t = 120 min are observed for all offspring groups. The levels of the female groups are almost equal, whereas the male groups (A), (B), and (C) tend to differ at t = 30 min.
Fig. 3. Mean and standard deviation (as error bars) of plasma glucose G(t) during IPGTT for all groups (A) – (F) at 3 weeks of age (male and female offspring).
At 11 weeks of age (Fig. 4), the observation is different: both negative control groups (G) and (K) of NDMs show an improved and physiological glucose tolerance with a peak value below 300 mg/dl and a complete remission after 120 min. The positive control groups (I) and (M), however, show a diabetic profile, with increased basal glucose levels and an incomplete remission. The experimental groups (H) and (L), in turn, present a characteristic that is different from that of both control groups: within the short-term reaction (15–45 min), glucose levels are increased similarly to the positive control groups, while on the long-term time scale (60–120 min), it decreases to the physiological values of the negative control groups.
Fig. 4. Mean and standard deviation (as error bars) of plasma glucose G(t) during IPGTT for all groups (G) – (M) at 11 weeks of age (male and female offspring).
In silico model-based predictors
The application of the in silico model allows condensing these qualitative observations into quantitative predictors. In Table 1, selected combined groups are considered, and the mean and standard deviation for the model-based predictors {G basal , k G1, k G2} are shown.
Table 1. Different IPGTT patterns are observed during weaning (offspring 3 weeks of age) as well as later (offspring 11 weeks of age) for negative control, positive control, and experimental groups. Means µ and standard deviations σ of combined groups are shown. The negative control group at 11 weeks of age may serve as a reference (gray background)
The best values are obtained in the negative control group at 11 weeks of age (line 1). The mean basal glucose value G basal is low, and the glucose sensitivities k G1 and k G2 are high. This case may serve as a reference and is most similar to the human reference values (line 5). The experimental group (line 2) shows an elevated G basal and a slightly reduced k G2, which is still sufficient for remission in the IPGTT. However, it is characterized by a small k G1 that causes a distinct peak in IPGTT. The positive control group (line 3) shows a high value of G basal combined with minimum values of k G1 and k G2, which describes a diabetic profile.
During weaning at 3 weeks of age, G basal is slightly elevated and k G1 is reduced (line 4 compared to line 1). However, the long-term glucose sensitivity k G2 performs better, which leads to a stable remission in IPGTT.
Pooled predictors and their effects
To assess these observations, the effects and significances of pooled predictors are summarized in Table 2 for different impacts. During weaning at 3 weeks of age, the effects between the experimental and both control groups are small and (with one exception) not significant (lines 1–3). In contrast, all effects are significant at 11 weeks of age (lines 4–6). In the experimental group, G basal is elevated compared to the negative control group (line 4) but is much better than that in the positive control group (line 5). Gains k G1 and k G2 are severely degraded in the experimental group compared to the negative control group (line 4) but are still better than that in the positive control group (line 5). Line 6 just proves significant differences between both control groups; its effects are equal to line 4 minus line 5. Finally, the impact of offspring sex is analyzed in lines 7 and 8. None of the effects are significant; nevertheless, k G2 has the highest level of significance and will be considered for sex-specific classification in the second approach of the next section.
Table 2. Effects e of the predictors {G basal, k G1, k G2} and their levels of significance P e are shown. Significant predictors with a level of P e ≤ 0.05 are printed in bold.
Classification of individual predictors
An alternative to pooled predictor results can be obtained from the individual predictors, which are plotted in Fig. 5a for the subjects at 11 weeks of age in the three-dimensional predictor space for {G basal , k G1, k G2}. At first glance, one can see a possible separation of clusters.
Fig. 5. (a) Predictors {G basal, k G1, k G2} of n = 45 individual subjects of groups (G) – (M) as marks in the predictor space, (b) classification tree for three groups with (c) corresponding confusion matrix, and (d) classification tree for six groups with (e) corresponding confusion matrix.
Based on these data, we automatically generated classification trees. As a first approach, a classification into three groups (negative control, experimental, and positive control) regarding maternal imprinting was performed. The obtained tree is shown in Fig. 5b. As a first criterion, subjects with G basal > 170 will be assigned to the positive control group (= genetically determined); otherwise, they will be assigned to the negative control group (= healthy) in the case of k G1 > 4.4 yields; otherwise, they will be assigned to the experimental group. Apparently, k G2 does not have an impact. As the confusion matrix in Fig. 5c shows, P c = 41/45 = 91.1% of the subjects are classified correctly with these two simple rules (specificity regarding experimental group is 11/12 = 91.7%, sensitivity regarding negative control group is 17/20 = 85.0%).
As a second approach, we additionally distinguish male and female subjects, which leads to a total of six groups. The automatic generation results in a more complex classification tree, as shown in Fig. 5d. The most important predictors are still G basal and k G1, although they have changed their order. Additionally, k G2 comes into play, and it decides between sexes at the final stage. The confusion matrix in Fig. 5e proves that P c = 37/45 = 82.2% of the subjects can still be classified correctly.
Discussion
Proof of trans-generational diabetic programming
At 11 weeks of age, the experimental groups showed a specific metabolic behavior that differed significantly from both control groups. Mice of the negative control groups (G, K) and the experimental groups (H, L) are both not genetically programmed by Mendelian inheritance. Therefore, the reason for the different characteristics in the IPGTT and in the in silico model-based predictors must be located in the diabetic in utero milieu of the offspring. The difference between NDMs and DMs causes the observed trans-generational diabetic programming.
What are the underlying mechanisms? Experimental groups (H, L) did not show long-term glucose intolerances. The basal glucose levels as well as the levels after t = 60 min are in the physiological range specified by the control groups (G, K), see Fig. 4. This is confirmed by the predictors G basal as well as k G2, respectively (see Table 2, line 4). Hence, glucose clearance or disposal follows different mechanisms compared to diabetic subjects in the positive control groups (I, M).
However, the short-term or first-phase response is disturbed (early peak in IPGTT in Fig. 4, decreased k G1 in Table 2, line 4, and classification rule based on k G1 in Fig. 5b). It is insulin mediated and may be caused by an altered reaction of the β-cells of the pancreas. Taking these observations together, we can conclude that the diabetic metabolism of mothers leads to altered insulin sensitivity as well as abnormal glucose-stimulated insulin release in offspring.
In the course of analyzing features of trans-generational diabetic programming in preliminary experiments, it could also be presented that early altered insulin sensitivity as well as abnormal glucose-stimulated insulin release is the part of diabetic mal-programming. Moreover, pancreases of wild-type offspring of DMs showed a significantly lower pancreas mass and more uncoordinated islet organizations as well as morphological β-cell and islet alterations compared to the offspring of NDMs, which is in line with Reusens et al. Reference Reusens, Ozanne and Remacle14
The difference in programming in the experimental groups in relation to nondiabetic controls would remain undiscovered if only fasting glucose measurements (Fig. 4) were considered. To detect the altered insulin sensitivity as well as abnormal glucose-stimulated insulin release, the IPGTT glucose must be evaluated at t = 15, 30 min (Fig. 4), or even better the predictor k G1 has to be assessed. This is clearly confirmed by the effect of predictor k G1 in Table 2, line 4: by diabetic programming, a drop of –11.428 for k G1 is predicted with high significance.
This observation is different from genetically programming by Mendelian inheritance, which can be easily detected by looking at fasting glucose levels in Fig. 4. The corresponding predictor G basal showed an effect of +202.488 mg/dl for groups (I, M) compared to (G, K) with high significance.
Impact of weaning
During the suckling period at 3 weeks of age, almost no significant differences between groups (A) – (F) were detected. Therefore, as already reported, suckling may have a protective effect targeting glucose homeostasis in offspring and mothers. Reference Martens, Shafer and Dean15 In Table 1, the mean values of the combined offspring groups during weaning can be compared with the later groups. Note that in the negative control groups, glucose tolerance is improved even after weaning. If we take this together with the previous section, diabetic programming receives verifiable effects during fetal stages but becomes apparent in offspring metabolism after weaning. Reference Garofano, Czernichow and Bréant16
Sex-specific differences
Compared to the impacts of diabetic programming and weaning that were discussed before, sex-specific differences seem to be less dominant. No significant effects can be observed when combined female groups are compared to combined male groups, see Table 2, lines 7, 8. At 11 weeks of age, female plasma glucose levels G in t = 30 and 45 min were lower than male levels (see Fig. 4). This observation is confirmed by the classification tree in Fig. 5d that uses k G2 to distinguish the female and male groups. In general, the second-phase glucose tolerance seems to be advantageous in females compared to males.
Conclusions
We show significant trans-generational impacts by analyzing diabetic programming patterns, which are clearly not genetically programmed by Mendelian inheritance (experimental group). These novel insights show that trans-generational diabetic programming leads to an evident change of patterns within the glucose insulin homeostasis in the next generations. The corresponding predictor k G1 is highly significant.
The picture is clearly different from trans-generational genetically determined diabetes patterns (positive control group), which lead to significantly raised basal glucose values, as the predictor G basal shows.
Depending on both predictors k G1 and G basal obtained from the individual in silico model of offspring, 91% of the subjects can be classified correctly with respect to maternal imprinting. We conclude, therefore, that maternal diabetes per se is a strong risk factor leading to alterations within glucose homeostasis and diabetes in their offspring early on.
The newly established dynamic in vivo and in silico models are suitable and highly sensitive for an individual early diagnosis of specific pathophysiological changes, trans-generational as well as for both generations. The model-based predictors proved to be appropriate to determine significant effects even for smaller group sizes and to successfully set up a diagnostic classification tree.
Moreover, our approach is well suited to diagnose pathophysiological changes early on to predict personalized developments and to start preventive therapies for both generations early Reference Smith, Nathan, Arslanian, Groop, Rizza and Rotter17 to assess specific maternal interventions, for example, a particular immunization as a possible therapeutic approach. Reference Eberle, Merki and Yamashita18
Acknowledgments
The authors thank the teams of the Diabetes Center and Department of Internal Medicine IV of the Ludwig-Maximilians University of Munich (LMU) for support of the in vivo part of this work.
Financial Support
Partially funded by the “Förderprogramm für Forschung und Lehre (FöFoLe)” (projects 648/625 and 63/2009) of the Faculty of Medicine of the LMU, by the Friedrich-Baur-Stiftung (project 34/09), by the “Münchner Medizinische Wochenschrift (MMW) e.V.”, and by the “Deutsche Diabetes Gesellschaft (DDG)”.
Conflicts of Interest
None.
Ethical standards
The authors assert that all procedures contributing to this work comply with the ethical standards of the relevant national guides on the care and use of laboratory animals (German Animal Welfare Act) and has been approved by the Federal Government of Upper Bavaria.
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