Computational model of excitable cell indicates ATP free energy dynamics in response to calcium oscillations are undampened by cytosolic ATP buffers

Computational approaches for understanding energy metabolism

There has been a surge of interest in understanding the regulation of metabolic networks involved in disease in recent years. Quantitative models are increasingly being used to interrogate the metabolic pathways that are contained within this complex disease biology. At the core of this effort is the mathematical modeling of central carbon metabolism involving glycolysis and the citric acid cycle (referred to as energy metabolism). Here, we discuss several approaches used to quantitatively model metabolic pathways relating to energy metabolism and discuss their formalisms, successes, and limitations.

Modeling and analysis of biopathways dynamics

Cellular processes are governed and coordinated by a multitude of biopathways. A pathway can be viewed as a complex network of biochemical reactions. The dynamics of this network largely determines the functioning of the pathway. Hence the modeling and analysis of biochemical networks dynamics is an important problem and is an active area of research. Here we review quantitative models of biochemical networks based on ordinary differential equations (ODEs). We mainly focus on the parameter estimation and sensitivity analysis problems and survey the current methods for tackling them. In this context we also highlight a recently developed probabilistic approximation technique using which these two problems can be considerably simplified.

Computational modeling of mitochondrial energy transduction

Mitochondria are the power plant of the heart, burning fat and sugars to supply the muscle with the adenosine triphosphate (ATP) free energy that drives contraction and relaxation during each heart beat. This function was first captured in a mathematical model in 1967. Today, interest in such a model has been rekindled by ongoing in silico integrative physiology efforts such as the Cardiac Physiome project. Here, the status of the field of computational modeling of mitochondrial ATP synthetic function is reviewed.

Similar mitochondrial activation kinetics in wild-type and creatine kinase-deficient fast-twitch muscle indicate significant Pi control of respiration

Past simulations of oxidative ATP metabolism in skeletal muscle have predicted that elimination of the creatine kinase (CK) reaction should result in dramatically faster oxygen consumption dynamics during transitions in ATP turnover rate. This hypothesis was investigated. Oxygen consumption of fast-twitch (FT) muscle isolated from wild-type (WT) and transgenic mice deficient in the myoplasmic (M) and mitochondrial (Mi) CK isoforms (MiM CK(-/-)) were measured at 20°C at rest and during electrical stimulation. MiM CK(-/-) muscle oxygen consumption activation kinetics during a step change in contraction rate were 30% faster than WT (time constant 53 ± 3 vs. 69 ± 4 s, respectively; mean ± SE, n = 8 and 6, respectively). MiM CK(-/-) muscle oxygen consumption deactivation kinetics were 380% faster than WT (time constant 74 ± 4 s vs. 264 ± 4 s, respectively). Next, the experiments were simulated using a computational model of the oxidative ATP metabolic network in FT muscle featuring ADP and Pi feedback control of mitochondrial respiration (J. A. L. Jeneson, J. P. Schmitz, N. A. van den Broek, N. A. van Riel, P. A. Hilbers, K. Nicolay, J. J. Prompers. Am J Physiol Endocrinol Metab 297: E774-E784, 2009) that was reparameterized for 20°C. Elimination of Pi control via clamping of the mitochondrial Pi concentration at 10 mM reproduced past simulation results of dramatically faster kinetics in CK(-/-) muscle, while inclusion of Pi control qualitatively explained the experimental observations. On this basis, it was concluded that previous studies of the CK-deficient FT muscle phenotype underestimated the contribution of Pi to mitochondrial respiratory control.

In vivo 31P MRS detection of an alkaline inorganic phosphate pool with short T1 in human resting skeletal muscle

Non-invasive determination of mitochondrial content is an important objective in clinical and sports medicine. 31P MRS approaches to obtain information on this parameter at low field strength typically require in-magnet exercise. Direct observation of the intra-mitochondrial inorganic phosphate (Pi) pool in resting muscle would constitute an alternative, simpler method. In this study, we exploited the higher spectral resolution and signal-to-noise at 7T to investigate the MR visibility of this metabolite pool. 31P in vivo MR spectra of the resting soleus (SOL) muscle were obtained with 1H MR image-guided surface coil localization (six volunteers) and of the SOL and tibialis anterior (TA) muscle using 2D CSI (five volunteers). A resonance at a frequency 0.38 ppm downfield from the cytosolic Pi resonance (Pi(1); pH 7.0 ± 0.04) was reproducibly detected in the SOL muscle in all subjects and conditionally attributed to the intra-mitochondrial Pi pool (Pi(2); pH 7.3 ± 0.07). In the SOL muscle, the Pi(2)/Pi(1) ratio was 1.6 times higher compared to the TA muscle in the same individual. Localized 3D CSI results showed that the Pi(2) peak was present in voxels well away from blood vessels. Determination of the T1 of the two Pi pools in a single individual using adiabatic excitation of the spectral region around 5 ppm yielded estimates of 4.3 ± 0.4 s vs 1.4 ± 0.5 s for Pi(1) and Pi(2), respectively. Together, these results suggest that the intra-mitochondrial Pi pool in resting human skeletal muscle may be visible with 31P MRS at high field.

Magnitude and control of mitochondrial sensitivity to ADP

The transduction function for ADP stimulation of mitochondrial ATP synthesis in skeletal muscle was reconstructed in vivo and in silico to investigate the magnitude and origin of mitochondrial sensitivity to cytoplasmic ADP concentration changes. Dynamic in vivo measurements of human leg muscle phosphocreatine (PCr) content during metabolic recovery from contractions were performed by (31)P-NMR spectroscopy. The cytoplasmic ADP concentration ([ADP]) and rate of oxidative ATP synthesis (Jp) at each time point were calculated from creatine kinase equilibrium and the derivative of a monoexponential fit to the PCr recovery data, respectively. Reconstructed [ADP]-Jp relations for individual muscles containing more than 100 data points were kinetically characterized by nonlinear curve fitting yielding an apparent kinetic order and ADP affinity of 1.9 +/- 0.2 and 0.022 +/- 0.003 mM, respectively (means +/- SD; n = 6). Next, in silico [ADP]-Jp relations for skeletal muscle were generated using a computational model of muscle oxidative ATP metabolism whereby model parameters corresponding to mitochondrial enzymes were randomly changed by 50-150% to determine control of mitochondrial ADP sensitivity. The multiparametric sensitivity analysis showed that mitochondrial ADP ultrasensitivity is an emergent property of the integrated mitochondrial enzyme network controlled primarily by kinetic properties of the adenine nucleotide translocator.

Multi-element probabilistic collocation for sensitivity analysis in cellular signalling networks

The multi-element probabilistic collocation method (ME-PCM) as a tool for sensitivity analysis of differential equation models as applied to cellular signalling networks is formulated. This method utilises a simple, efficient sampling algorithm to quantify local sensitivities throughout the parameter space. The application of the ME-PCM to a previously published ordinary differential equation model of the apoptosis signalling network is presented. The authors verify agreement with the previously identified regions of sensitivity and then go on to analyse this region in greater detail with the ME-PCM. The authors demonstrate the generality of the ME-PCM by studying sensitivity of the system using a variety of biologically relevant markers in the system such as variation in one (or many) chemical species as a function of time, and total exposure of a single chemical species.

The fully integrated biomedical engineering programme at Eindhoven University of Technology

The development of a fully integrated biomedical engineering programme (life sciences included from the start) is described. Details are provided about background, implementation, and didactic concept: design centred learning combined with courses. The curriculum has developed into a bachelor—master's programme with two different master's degrees: Master's Degree in Biomedical Engineering and Master's Degree in Medical Engineering. Recently, the programme has adopted semester programming, has included a major and minor in the bachelor's degree phase, and a true bachelor's degree final project. Details about the programme and data about where graduates find jobs are provided in this paper.

Computational modelling identifies the impact of subtle anatomical variations between amphibian and mammalian skeletal muscle on spatiotemporal calcium dynamics

The physical sites of calcium entry and exit in the skeletal muscle cell are distinct and highly organised in space. It was investigated whether the highly structured spatial organisation of sites of Ca(2+) release, uptake and action in skeletal muscle cells substantially impacts the dynamics of cytosolic Ca(2+) handling and thereby the physiology of the cell. Hereto, the spatiotemporal dynamics of the free calcium distribution in a fast-twitch (FT) muscle sarcomere was studied using a reaction-diffusion computational model for two genotypes with known anatomical differences. A computational model of a murine FT muscle sarcomere is developed, de novo including a closed calcium mass balance to simulate spatiotemporal high stimulation frequency calcium dynamics at 35 degrees C. Literature data on high-frequency calcium dye measurements were used as a first step towards model validation. The murine and amphibian sarcomere models were phenotypically distinct to capture known differences in positions of troponin C, actin-myosin overlap and calcium release within the sarcomere between frog and mouse. The models predicted large calcium gradients throughout the myoplasm as well as differences in calcium concentrations near the mitochondria of frog and mouse. Furthermore, the predicted Ca(2+) concentration was high at positions where Ca(2+) has a regulatory function, close to the mitochondria and troponin C.