Effects of glycemic control on glucose utilization and mitochondrial respiration during resuscitated murine septic shock

Background This study aims to test the hypothesis whether lowering glycemia improves mitochondrial function and thereby attenuates apoptotic cell death during resuscitated murine septic shock. Methods Immediately and 6 h after cecal ligation and puncture (CLP), mice randomly received either vehicle or the anti-diabetic drug EMD008 (100 μg · g-1). At 15 h post CLP, mice were anesthetized, mechanically ventilated, instrumented and rendered normo- or hyperglycemic (target glycemia 100 ± 20 and 180 ± 50 mg · dL-1, respectively) by infusing stable, non-radioactive isotope-labeled 13C6-glucose. Target hemodynamics was achieved by colloid fluid resuscitation and continuous i.v. noradrenaline, and mechanical ventilation was titrated according to blood gases and pulmonary compliance measurements. Gluconeogenesis and glucose oxidation were derived from blood and expiratory glucose and 13CO2 isotope enrichments, respectively; mathematical modeling allowed analyzing isotope data for glucose uptake as a function of glycemia. Postmortem liver tissue was analyzed for HO-1, AMPK, caspase-3, and Bax (western blotting) expression as well as for mitochondrial respiratory activity (high-resolution respirometry). Results Hyperglycemia lowered mitochondrial respiratory capacity; EMD008 treatment was associated with increased mitochondrial respiration. Hyperglycemia decreased AMPK phosphorylation, and EMD008 attenuated both this effect as well as the expression of activated caspase-3 and Bax. During hyperglycemia EMD008 increased HO-1 expression. During hyperglycemia, maximal mitochondrial oxidative phosphorylation rate was directly related to HO-1 expression, while it was unrelated to AMPK activation. According to the mathematical modeling, EMD008 increased the slope of glucose uptake plotted as a function of glycemia. Conclusions During resuscitated, polymicrobial, murine septic shock, glycemic control either by reducing glucose infusion rates or EMD008 improved glucose uptake and thereby liver tissue mitochondrial respiratory activity. EMD008 effects were more pronounced during hyperglycemia and coincided with attenuated markers of apoptosis. The effects of glucose control were at least in part due to the up-regulation of HO-1 and activation of AMPK. Electronic supplementary material The online version of this article (doi:10.1186/2197-425X-2-19) contains supplementary material, which is available to authorized users.


Modeling approach
In the follwing we derive formulas to estimate gluconeogenesis and glucose uptake from plasma tracer enrichments obtained from a constant infusion of a mixture of unlabeled and 13 C 6 labeled glucose assuming metabolic steady state conditions. The analysis of the resulting tracer enrichment in plasma is based on the metabolic structure shown in fig 1. The infused tracer is diluted by endogenous glucose production, whose rate is denoted as GN G (gluconeogenesis). Let x * be the amount of labeled and x 0 that of unlabeled glucose in plasma. For the mole fraction of labeled material one obtains: x * x * +x 0 ; Figure 1: structure of the model used to evaluate 13 C-Tracer data: A one pool model is assumed, with the plasma glucose pool as central, whole body compartment. Gluconeogenesis feeds into this pool, and glucose uptake starts from it. Glucose uptake is controlled by glucose concentration and AMPK activation. In a simplified version, AMPK activation is triggered by glycemic effects, and hence glycemia exhibits a direct and an indirect, AMPK mediated effect. inp o , inp * : Exogenous input of unlabeled (inp o ) and labeled (inp * ) glucose.
With inp * as the infusion rate of the labeled glucose the rate of gluconeogenesis can be estimated from the mole fraction of the labelled plasma glucose [1] as: Based on model structure shown in fig 1 the combined glucose input and GN G matches its whole body uptake and the following balance holds: To relate GN G and uptake values, estimated from tracer data to measurements of glucose concentration (x) and AMPK stimulation(z) the GN G and glucose uptake rates are expressed as a linear functions: With the proposed linearity the balances above also hold for the mean values of an experimental group and one can subtract the eqns 3 applied on group mean values from the same eqns, applied on a actual measurement set to obtain balances pertaining to 'centered values' as: ∆GN G = k 5 ∆x + k 6 ∆z (5) Where ∆ denotes the difference between actual value and group mean value. Measureable quantities are ∆GN G,∆x, ∆z, the input values are known from the experimental design. In the ideal case, there should be a set of coefficients k 2 , k 3 , k 5 and k 6 for which the measured quantities (∆GN G, ∆x and ∆z), satisfy the eqns 4 and 5 for each data set, after correction for measurement errors. Hence, a set of coefficients is searched, for which the corrected values satify eqns 4 and 5 and were these corrected values came as close a possible to measured values. This dual task is performed using an orthogonal regression. The regression used corresponds to standard orthogonal regression, that was extended such that the variables for concentration and flow rates as well as the the corrected values for glucose concentration and AMPK activation have to satisfy eqns 4 and 5. The approach was implemented with the bayesian statistical package stan [2], which can be considered be a further development of the established WINBUGS/BUGS program [3], the orthogonal regression was extended based on the example demonstrated in [4], chapter 14.1. The corresponding sourcescript is shown in the section 'Source code' below. In a first analysis the data were evaluated using a separate set of coefficients for the vehicle and imeglimin group. The first two columns of table 1 show the corresponding determined coefficients. There is a collinearity between concentration and AMPK measurements which precludes determining the coefficients pertaining to AMPK for a separate analysis for each group. Hence, the coefficients for AMPK were set to zero for a separate analyse. Figure 2a shows the resulting uptake curve predicted for different concentration values. When the same set of coefficients was applied simultaneously for the vehicle and the imeglimin group an impact of AMPK could be separated from a concentration effect. A functional dependency on two variables is difficult to display. However, in average there is a positive correlation between AMPK activation and glucose concentration for the imeglimin group and a negative correlation for the vehicle groups. This allows to approximate the AMPK activation as a function of the plasma glucose concentration as: ∆z = p 0 + p 1 ∆x.
The coefficients p 0 , p 1 were determined from the group mean values for AMPK activation and glucose concentration. Different coefficients were obtainef for the imeglimin and vehicle group. Inserting the approximated AMPK values into eqn 4, and using the coefficients, shown in the third column of table 1 gives separate relations to express the uptake as a direct function of the concentration and an indirect concentration effect, mediated by AMPK. As there were different AMPK/(glucose concentration) relations for the vehicle and imiglimin group, different curves were obtained for the two different groups. They are shown in fig 2b in the main body of the paper.

source code
The code below demonstrates a separate analysis of the imeglimin and vehicle group. For the implementation eqns 4 and 5 are combined and solved for the glucose concentration:  The following code holds for the case that k 6 = 0, or no impact of AMPK activation on gluconeogenesis. The code is used with the Stan package [2] that implements a Monte-Carlo, Marcov-Chain sampling algorithm, which in essence draws a series of random samples from the probability, that a set of flux rates and coefficients reflects the true values. The section 'model' defines the random processes and their interrelations, which are used to define the probability for flux rates and coefficients, given the measured values. The section 'generated quantities' calculates for the 'random draws' of coefficients uptake values as a function of concentration values. 10000 samples were drawn in this way and mean and quartile values were assessed from these 10000 samples.

data {
//definition of input data int<lower=0> Na; // number of cases for imeglimin group int<lower=0> Nb; // number of cases for vehicle group int<lower=0> N; // total number of cases // suffix a or _a refers to imeglimin group // suffix b or _b refers to vehicle group real gnga [