A simple model of cardiac mitochondrial respiration with experimental validation.

Cardiac mitochondria are intracellular organelles that play an important role in energy metabolism and cellular calcium regulation. In particular, they influence the excitation-contraction cycle of the heart cell. A large number of mathematical models have been proposed to better understand the mitochondrial dynamics, but they generally show a high level of complexity, and their parameters are very hard to fit to experimental data. We derived a model based on historical free energy-transduction principles, and results from the literature. We proposed simple expressions that allow to reduce the number of parameters to a minimum with respect to the mitochondrial behavior of interest for us. The resulting model has thirty-two parameters, which are reduced to twenty-three after a global sensitivity analysis of its expressions based on Sobol indices. We calibrated our model to experimental data that consists of measurements of mitochondrial respiration rates controlled by external ADP additions. A sensitivity analysis of the respiration rates showed that only seven parameters can be identified using these observations. We calibrated them using a genetic algorithm, with five experimental data sets. At last, we used the calibration results to verify the ability of the model to accurately predict the values of a sixth dataset. Results show that our model is able to reproduce both respiration rates of mitochondria and transitions between those states, with very low variability of the parameters between each experiment. The same methodology may apply to recover all the parameters of the model, if corresponding experimental data were available.

Cell membrane permeabilization by 12-ns electric pulses: Not a purely dielectric, but a charge-dependent phenomenon.

Electric pulses of a few nanoseconds in duration can induce reversible permeabilization of cell membrane and cell death. Whether these effects are caused by ionic or purely dielectric phenomena is still discussed. We address this question by studying the impact of conductivity of the pulsing buffer on the effect of pulses of 12 ns and 3.2 MV/m on the DC-3F mammalian cell line. When pulses were applied in a high-conductivity medium (1.5 S/m), cells experienced both reversible electropermeabilization and cell death. On the contrary, no effect was observed in the low-conductivity medium (0.1 S/m). Possible artifacts due to differences in viscosity, temperature increase or electrochemical reactions were excluded. The influence of conductivity reported here suggests that charges still play a role, even for 12-ns pulses. All theoretical models agree with this experimental observation, since all suggest that only high-conductivity medium can induce a transmembrane voltage high enough to induce pore creation, in turn. However, most models fail to describe why pulse accumulation is experimentally required to observe biological effects. They mostly show no increase of permeabilization with accumulation of pulses. Currently, only one model properly describes pulse accumulation by modeling diffusion of the altered membrane regions.

Cell scale modeling of electropermeabilization by periodic pulses.

In this paper, we focus on the behaviour of periodic solutions to a cell-scale electropermeabilization model previously proposed by Kavian et al. [6]. Since clinical permeabilization protocols mostly submit cancer cells to trains of periodic pulses, we investigate on parameters that modify significantly the resulting permeabilization. Theoretical results of existence and uniqueness of periodic solutions are presented, for two different models of membrane electric conductivity. Numerical simulations were performed to corroborate these results and illustrate the asymptotic convergence to periodic solutions, as well as the dependency on biological parameters such as the cell size and the extracellular conductivity.

"Classical" electropermeabilization modeling at the cell scale.

The aim of this paper is to provide new models of cell electropermeabilization involving only a few parameters. A static and a dynamical model, which are based on the description of the electric potential in a biological cell, are derived. Existence and uniqueness results are provided for each differential system, and an accurate numerical method to compute the solution is described. We then present numerical simulations that corroborate the experimental observations, providing the consistency of the modeling. We emphasize that our new models involve very few parameters, compared with the most achieved models of Neu and Krassowska (Phys Rev E 53(3):3471-3482, 1999) and DeBruin and Krassowska (Biophys J 77:1225-1233, 1999), but they provide the same qualitative results. Thus, these models will facilitate drastically the forthcoming inverse problem solving, which will consist in fitting them with the experiments.

Hybrid molecular mechanics/coarse-grained simulations for structural prediction of G-protein coupled receptor/ligand complexes.

Understanding how ligands bind to G-protein coupled receptors (GPCRs) provides insights into a myriad of cell processes and is crucial for drug development. Here we extend a hybrid molecular mechanics/coarse-grained (MM/CG) approach applied previously to enzymes to GPCR/ligand complexes. The accuracy of this method for structural predictions is established by comparison with recent atomistic molecular dynamics simulations on the human ß2 adrenergic receptor, a member of the GPCRs superfamily. The results obtained with the MM/CG methodology show a good agreement with previous all-atom classical dynamics simulations, in particular in the structural description of the ligand binding site. This approach could be used for high-throughput predictions of ligand poses in a variety of GPCRs.