Yann Bouret

Na+/H+ antiporter (NHE1) and lactate/H+ symporters (MCTs) in pH homeostasis and cancer metabolism

The Na(+)/H(+)-exchanger NHE1 and the monocarboxylate transporters MCT1 and MCT4 are crucial for intracellular pH regulation, particularly under active metabolism. NHE1, a reversible antiporter, uses the energy provided by the Na(+) gradient to expel H(+) ions generated in the cytosol. The reversible H(+)/lactate(-) symporters MCT1 and 4 cotransport lactate and proton, leading to the net extrusion of lactic acid in glycolytic tumors. In the first two sections of this article we review important features and remaining questions on the structure, biochemical function and cellular roles of these transporters. We then use a fully-coupled mathematical model to simulate their relative contribution to pH regulation in response to lactate production, as it occurs in highly hypoxic and glycolytic tumor cells. This article is part of a Special Issue entitled: Mitochondrial Channels edited by Pierre Sonveaux, Pierre Maechler and Jean-Claude Martinou.

Bootstrap and permutation tests of independence for point processes

Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce non-parametric test statistics, which are rescaled general

A dynamical model for the Utricularia trap

U

Application of quasi-degenerate perturbation theory to the calculation of rotational energy levels of methane vibrational polyads.

-statistics, whose corresponding critical values are constructed from bootstrap and randomization/permutation approaches, making as few assumptions as possible on the underlying distribution of the point processes. We derive general consistency results for the bootstrap and for the permutation w.r.t. to Wassersteins metric, which induce weak convergence as well as convergence of second order moments. The obtained bootstrap or permutation independence tests are thus proved to be asymptotically of the prescribed size, and to be consistent against any reasonable alternative. A simulation study is performed to illustrate the derived theoretical results, and to compare the performance of our new tests with existing ones in the neuroscientific literature.

Capturing Intracellular pH Dynamics by Coupling Its Molecular Mechanisms within a Fully Tractable Mathematical Model

We propose a model that captures the dynamics of a carnivorous plant, Utricularia inflata. This plant possesses tiny traps for capturing small aquatic animals. Glands pump water out of the trap, yielding a negative pressure difference between the plant and its surroundings. The trap door is set into a meta-stable state and opens quickly as an extra pressure is generated by the displacement of a potential prey. As the door opens, the pressure difference sucks the animal into the trap. We write an ODE model that captures all the physics at play. We show that the dynamics of the plant is quite similar to neuronal dynamics and we analyse the effect of a white noise on the dynamics of the trap.

Study of the thrust–drag balance with a swimming robotic fish

In previous works, we have introduced an alternative perturbation scheme to find approximate solutions of the spectral problem for the rotation-vibration molecular Hamiltonian. An important feature of our approach is that the zero order Hamiltonian is the direct product of a purely vibrational Hamiltonian with the identity on the rotational degrees of freedom. The convergence of our method for the methane vibrational ground state was very satisfactory and our predictions were quantitative. In the present article, we provide further details on the implementation of the method in the degenerate and quasi-degenerate cases. The quasi-degenerate version of the method is tested on excited polyads of methane, and the results are assessed with respect to a variational treatment. The optimal choice of the size of quasi-degenerate spaces is determined by a trade-off between speed of convergence of the perturbation series and the computational effort to obtain the effective super-Hamiltonian.

Reconstructing the functional connectivity of multiple spike trains sing Hawkes models

We describe the construction of a fully tractable mathematical model for intracellular pH. This work is based on coupling the kinetic equations depicting the molecular mechanisms for pumps, transporters and chemical reactions, which determine this parameter in eukaryotic cells. Thus, our system also calculates the membrane potential and the cytosolic ionic composition. Such a model required the development of a novel algebraic method that couples differential equations for slow relaxation processes to steady-state equations for fast chemical reactions. Compared to classical heuristic approaches based on fitted curves and ad hoc constants, this yields significant improvements. This model is mathematically self-consistent and allows for the first time to establish analytical solutions for steady-state pH and a reduced differential equation for pH regulation. Because of its modular structure, it can integrate any additional mechanism that will directly or indirectly affect pH. In addition, it provides mathematical clarifications for widely observed biological phenomena such as overshooting in regulatory loops. Finally, instead of including a limited set of experimental results to fit our model, we show examples of numerical calculations that are extremely consistent with the wide body of intracellular pH experimental measurements gathered by different groups in many different cellular systems.

Ab initio effective rotational Hamiltonians: A comparative study

A robotic fish is used to test the validity of a simplification made in the context of fish locomotion. With this artificial aquatic swimmer, we verify that the momentum equation results from a simple balance between a thrust and a drag that can be treated independently in the small amplitude regime. The thrust produced by the flexible robot is proportional to A2f2, where A and f are the respective tail-beat amplitude and oscillation frequency, irrespective of whether or not f coincides with the resonant frequency of the fish. The drag is proportional to U02, where U0 is the swimming velocity. These three physical quantities set the value of the Strouhal number in this regime. For larger amplitudes, we found that the drag coefficient is not constant but increases quadratically with the fin amplitude. As a consequence, the achieved locomotion velocity decreases, or the Strouhal number increases, as a function of the fin amplitude.A robotic fish is used to test the validity of a simplification made in the context of fish locomotion. With this artificial aquatic swimmer, we verify that the momentum equation results from a simple balance between a thrust and a drag that can be treated independently in the small amplitude regime. The thrust produced by the flexible robot is proportional to A2f2, where A and f are the respective tail-beat amplitude and oscillation frequency, irrespective of whether or not f coincides with the resonant frequency of the fish. The drag is proportional to U02, where U0 is the swimming velocity. These three physical quantities set the value of the Strouhal number in this regime. For larger amplitudes, we found that the drag coefficient is not constant but increases quadratically with the fin amplitude. As a consequence, the achieved locomotion velocity decreases, or the Strouhal number increases, as a function of the fin amplitude.

Inertial Mass Transport and Capillary Hydraulic Jump in a Liquid Foam Microchannel

BACKGROUND Statistical models that predict neuron spike occurrence from the earlier spiking activity of the whole recorded network are promising tools to reconstruct functional connectivity graphs. Some of the previously used methods are in the general statistical framework of the multivariate Hawkes processes. However, they usually require a huge amount of data, some prior knowledge about the recorded network, and/or may produce an increasing number of spikes along time during simulation. NEW METHOD Here, we present a method, based on least-square estimators and LASSO penalty criteria, for a particular class of Hawkes processes that can be used for simulation. RESULTS Testing our method on small networks modeled with Leaky Integrate and Fire demonstrated that it efficiently detects both excitatory and inhibitory connections. The few errors that occasionally occur with complex networks including common inputs, weak and chained connections, can be discarded based on objective criteria. COMPARISON WITH EXISTING METHODS With respect to other existing methods, the present one allows to reconstruct functional connectivity of small networks without prior knowledge of their properties or architecture, using an experimentally realistic amount of data. CONCLUSIONS The present method is robust, stable, and can be used on a personal computer as a routine procedure to infer connectivity graphs and generate simulation models from simultaneous spike train recordings.