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Cloutier et al., (2009). An integrative dynamic model of brain energy metabolism using in vivo neurochemical measurements.

August 2015, model of the month by Felix Winter
Original models: BIOMD0000000554.


Introduction

The metabolic response to neuronal stimulation is organized by the close interaction between neurons and astrocytes in the brain. Historically, kinetic models of the brain energy metabolism have relied either on in vitro data or on parameters measured in other cell types. The model by Cloutier et al., [1, BIOMD0000000554], uses for the first time in vitro data of glucose and lactate dynamics in rat brains to calibrate the parameters of the kinetic equations and validate the model predictions. The model is used to predict the metabolic response to two different stimulation regimes and highlights the importance of astrocytic glycogen and the astrocyte-neuron-lactate shuttle (ANLS).


The Model

The model describes the metabolic response to a neuronal stimulation using the four compartments astrocytes, neurons, extracellular space and the capillary transport system. The four compartments are coupled via transport reactions for glucose, lactate, oxygen and carbon dioxide which enter and leave the system via the capillaries. Additional transport reactions describe the passive sodium inflow and active export of sodium in both astrocytes and neurons (Figure 1).

The data used to calibrate the model (Figure 2) have been measured using microelectrochemical sensors during perturbation experiments and have been published earlier [2, 3].

Figure 2

Figure 2Extracellular concentration of glucose and lactate in response to the tail pinch experiment. Experimental data for these two metabolites has been used to calibrate the parameters of the kinetic models. This figure corresponds to Figure 2f and 2i in the original paper [1]. The figure was reproduced by simulating BIOMD0000000554 using Copasi v4.16.

Results

Using the in vivo data from different experiments to calibrate and validate the model, the authors were able to reproduce experimentally determined data with very high accuracy. The inclusion of glycogen breakdown is identified as the key step in reproducing the parallel increase in extracellular glucose and extracellular lactate. The model is validated against data measured in astrocytes treated with propanolol and subsequently modified to predict the metabolic response to a restraint experiment.


Note:

The model available in BioModels has been imported from the CellML model repository and transformed into SBML. A close inspection of the equation reveals several differences between the model described in the paper and the model published in the repositories.

Most of the parameters encoded in the model differ only slightly from the values listed in Table 8 and Table 9 of the publication (Figure 3). These small differences are most likely the effect of numerical rounding to four decimal places. Other parameters differ by more than two orders of magnitude. The inconsistencies between the original (paper) version and repository version may be because of the changes that the authors have made to the model after the publication of the paper to make it work in line with the physiologically feasible performance. The model is therefore a prime example for the benefit given by the provision of the model in a machine-readable format in addition to the equations and parameter values listed in the paper.

Figure 1

Figure 1 SBGN map of all the metabolic and transport reactions considered in the model. The four compartments capillaries, extracellular space, neurons and astrocytes are described in the paper. The two compartments artery and venous balloon are part of the model but not mentioned in the paper. CellDesigner 4.3 was used to create the SBGN diagram.

Model history

The model was built on previous attempts to model the neuron-astrocytic interactions. Many of the ideas and equations are already present in a model by Aubert and Costalat [4, MODEL1411210000]. In addition to the metabolic response, the model of Aubert and Costalat also featured a description of the vascular response to neuronal stimulation using the so-called balloon model for the venous volume. The combination of the vascular and the metabolic response are used to calculate the blood-oxygen-level dependent (BOLD) signal which is still part of the SBML model but not described in the paper.

Figure 3

Figure 3Absolute value of the difference between parameter values given in the paper and parameter values encoded in the model in percent.

Bibliographic references

  1. Cloutier et al. An integrative dynamic model of brain energy metabolism using in vivo neurochemical measurements J Comput Neurosci. 27(3):391-414. 2009.
  2. Bolger et al. Real-time monitoring of brain extracellular lactate. In: Di Chiara G, Carboni E, Valentini V, Acquas E, Bassareo V, Cadoni C (eds) Monitoring molecules in neuroscience, University of Cagliari, Cagliari, Italy, p 286. 2006
  3. Fillenz and Lowry. Studies of the source of glucose in the extracellular compartment of the rat brain. Dev Neurosci. 20(4-5):365-8. 1998.
  4. Aubert and Costalat. Interaction between astrocytes and neurons studied using a mathematical model of compartmentalized energy metabolism. J. Cereb. Blood Flow Metab. 25(11):1476-90. 2005.
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