Cell Respiration

Dynamic Causal Modelling is a framework for fitting differential equation models of neuronal activity to brain imaging data using Bayesian inference. The DCM approach can be applied to functional Magnetic Resonance Imaging (fMRI), Electroencephalographic (EEG), Magnetoencephalographic (MEG), and Local Field Potential (LFP) data [22] (link). The empirical work in this paper uses DCM for fMRI. DCMs for fMRI comprise a bilinear model for the neurodynamics and an extended Balloon model [23] (link) for the hemodynamics. The neurodynamics are described by the following multivariate differential equation where indexes continuous time and the dot notation denotes a time derivative. The th entry in corresponds to neuronal activity in the th region, and is the th experimental input.
A DCM is characterised by a set of ‘exogenous connections’, , that specify which regions are connected and whether these connections are unidirectional or bidirectional. We also define a set of input connections, , that specify which inputs are connected to which regions, and a set of modulatory connections, , that specify which intrinsic connections can be changed by which inputs. The overall specification of input, intrinsic and modulatory connectivity comprise our assumptions about model structure. This in turn represents a scientific hypothesis about the structure of the large-scale neuronal network mediating the underlying cognitive function. A schematic of a DCM is shown in Figure 1.
In DCM, neuronal activity gives rise to fMRI activity by a dynamic process described by an extended Balloon model [24] for each region. This specifies how changes in neuronal activity give rise to changes in blood oxygenation that are measured with fMRI. It involves a set of hemodynamic state variables, state equations and hemodynamic parameters, . In brief, for the th region, neuronal activity causes an increase in vasodilatory signal that is subject to autoregulatory feedback. Inflow responds in proportion to this signal with concomitant changes in blood volume and deoxyhemoglobin content . Outflow is related to volume through Grubb's exponent
[20] (link). The oxygen extraction is a function of flow where is resting oxygen extraction fraction. The Blood Oxygenation Level Dependent (BOLD) signal is then taken to be a static nonlinear function of volume and deoxyhemoglobin that comprises a volume-weighted sum of extra- and intra-vascular signals [20] (link)
where is resting blood volume fraction. The hemodynamic parameters comprise and are specific to each brain region. Together these equations describe a nonlinear hemodynamic process that converts neuronal activity in the th region to the fMRI signal (which is additionally corrupted by additive Gaussian noise). Full details are given in [20] (link),[23] (link).
In DCM, model parameters are estimated using Bayesian methods. Usually, the parameters are of greatest interest as these describe how connections between brain regions are dependent on experimental manipulations. For a given DCM indexed by , a prior distribution, is specified using biophysical and dynamic constraints [20] (link). The likelihood, can be computed by numerically integrating the neurodynamic (equation 1) and hemodynamic processes (equation 2). The posterior density is then estimated using a nonlinear variational approach described in [23] (link),[25] (link). Other Bayesian estimation algorithms can, of course, be used to approximate the posterior density. Reassuringly, posterior confidence regions found using the nonlinear variational approach have been found to be very similar to those obtained using a computationally more expensive sample-based algorithm [26] (link).

Clark electrode assays performed for comparative purposes utilized a Hansatech Oxytherm apparatus (PP Systems, Amesbury, MA) for rat heart mitochondria or a Rank system (Rank Brothers, Bottisham, Cambridge, England) for mouse liver mitochondria. For rat heart mitochondria, assays were performed in parallel with the same mitochondrial preparation, MAS, substrates and compounds as for the XF24 assays. Typically 62.5–125 µg of mitochondria were used in a volume of 500 µl MAS plus the appropriate substrate. Respiration was initiated by adding mitochondria, and followed by sequential addition of ADP, oligomycin and FCCP. Concentrations of substrate, ADP, oligomycin, and FCCP were identical to those used in the XF24 experiments. For mouse liver mitochondria, assays were performed in parallel the same mitochondrial preparation, MAS, substrates and compounds as for the XF24 assays with the following modifications: substrate was 5 mM succinate, 2 µM rotenone and 300 µM ADP was used. Typically, 0.3 mg/ml of mitochondria were used in a volume of 2.0–3.5 ml MAS plus the appropriate substrate. Respiration was initiated by adding mitochondria, followed by sequential addition of ADP, oligomycin and FCCP. Concentrations of oligomycin and FCCP were identical to those used in the XF24 experiments. Oxygen consumption rates were converted from nmol O/min/ml to pmol O₂/min/µg mitochondrial protein.

At the conclusion of the tick observations on day 8 post-attachment, fresh fecal samples were collected from each test deer pen. Additionally, internal tissues were collected from each deer in each treatment group. The deer were first sedated by injection of 1–2 mg/kg xylazine hydrochloride (100 mg/ml) into the large muscle bellies of the rump/rear limbs. While sedated, deer were euthanized by intravenous injection, administered via the jugular vein, of 86 mg/kg Euthasol (pentobarbital sodium, 390 mg/ml), resulting in pentobarbital sodium overdose. Death was confirmed by a combination of the following: (i) lack of heartbeat based on auscultation with a stethoscope; (ii) lack of respiration based on visual inspection of the thorax; (iii) lack of corneal reflex; and (iv) lack of response to firm toe pinch. All euthanasia was performed by the attending veterinarian exclusively.
Various tissues were collected from euthanized deer. The objective was to collect tissues similar to what would be collected by hunters when field dressing a killed deer. Thus, we focused on specific meat cuts, meat by-products and fatty tissues. Approximately 50 g of each tissue was surgically removed using disposable scalpels. Scalpels and surgical gloves were replaced between each individual tissue collection to minimize the risk of contamination. Each tissue was transferred to an individual biological specimen bag (Keefitt®), which was immediately stored at − 20 °C until analysis. In addition to collecting tissues from 16 deer in the treatment group, we collected tissues from two deer in the control group to establish a baseline and for analytical method development.
Tissues, plasma and feces were delivered to CSU for method development and analyses, and analyzed for the presence of fipronil and fipronil metabolites using validated methods of liquid chromatography/mass spectrometry (LC/MS). A list of tissue classifications, the maximum residue limits (MRL) listed by the US Environmental Protection Agency (EPA) for fipronil in cattle and the explicit tissue identifications are presented in Additional file 6: Table S2.
Critical study dates for each test deer (acclimation, exposure, post-attachment, capsule checks, tissue collection) are presented in Additional file 7: Table S3.