Ultrasensitivity and sharp threshold theorems for multisite systems

We study the ultrasensitivity of multisite binding processes where ligand molecules can bind to several binding sites, considering more particularly recent models involving complex chemical reactions in phosphorylation systems such as allosteric phosphorylation processes, or substrate-catalyst chain reactions and nucleosome mediated cooperativity. New statistics based formulas for the Hill coefficient and the effective Hill coefficient are provided and necessary conditions for a system to be ultrasensitive are exhibited. We then assume that the binding process is described by a density dependent birth and death process. We provide precise large deviation results for the steady state distribution of the process, and show that switch-like ultrasensitive responses are strongly related to the multi-stability of the associated dynamical system. Ultrasensitivity occurs if and only if the entropy of the dynamical system has more than one global minimum for some critical ligand concentration. In this case, the Hill coefficient is proportional to the number of binding sites, and the systems is highly ultrasensitive. We also discuss the interpretation of an extension $I_q$ of the effective Hill coefficient $I_{0.9}$ for which we recommend the computation of a broad range of values of $q$ instead of just the standard one corresponding to the 10% to 90% variation in the dose-response. It is shown that this single choice can sometimes mislead the conclusion by not detecting ultrasensitivity. This new approach allows a better understanding of multisite ultrasensitive systems and provides new tools for the design of such systems

Monte Carlo methods for light propagation in biological tissues

Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods in order to estimate the quantity of light that is received by a homogeneous tissue when emitted by an optic fiber. A variance reduction method is studied and implemented, as well as a Markov chain Monte Carlo method based on the Metropolis–Hastings algorithm. The resulting estimating methods are then compared to the so-called Wang–Prahl (or Wang) method. Finally, the formal representation allows to derive a non-linear optimization algorithm close to Levenberg–Marquardt that is used for the estimation of the scattering and absorption coefficients of the tissue from measurement

The effect of gap junctional coupling on the spatiotemporal patterns of Ca2+ signals and the harmonization of Ca2+-related cellular responses

The calcium ion (Ca²⁺), a universal signaling molecule, is widely recognized to play a fundamental role in the regulation of various biological processes. Agonist–evoked Ca²⁺ signals often manifest as rhythmic changes in the cytosolic free Ca²⁺ concentration (ccyt) called Ca²⁺ oscillations. Stimuli intensity was found to be proportional to the oscillation frequency and the evoked down-steam cellular response. Stochastic receptor expression in individual cells in a cell population inevitably leads to individually different oscillation frequencies and individually different Ca²⁺-related cellular responses. However, in many organs, the neighboring cells have to overcome their individually different sensitivity and produce a synchronized response. Gap junctions are integral membrane structures that enable the direct cytoplasmic exchange of Ca²⁺ ions and InsP₃ molecules between neighboring cells. By simulations, we were able to demonstrate how the strength of intercellular gap junctional coupling in relation to stimulus intensity can modify the spatiotemporal patterns of Ca²⁺ signals and harmonize the Ca²⁺-related cellular responses via synchronization of oscillation frequency. We demonstrate that the most sensitive cells are the wave initiator cells and that a highly sensitive region plays an important role in the determination of the Ca²⁺ phase wave direction. This sensitive region will then also progressively determine the global behavior of the entire system

Functional diversification of duplicate genes through subcellular adaptation of encoded proteins

Analysis of the subcellular localization patterns of duplicate genes revealed that protein subcellular adaptation represents a common mechanism for the functional diversification of duplicate genes

The feasibility of equilibria in large ecosystems: A primary but neglected concept in the complexity-stability debate

The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium feasibility vanishes in species rich systems. This result leaves us in the uncomfortable situation in which the existence of a feasible equilibrium assumed in local stability criteria is far from granted. We extend our analyses by changing interaction structure and intensity, and find that feasibility and stability is warranted irrespective of species richness with weak interactions. Interestingly, we find that the dynamical behaviour of ecologically inspired architectures is very different and richer than that of unstructured systems. Our results suggest that a general understanding of ecosystem dynamics requires focusing on the interplay between interaction strength and network architecture

Monte Carlo methods for light propagation in biological tissues

24 pages, 13 figures, arXiv:1311.5343Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods in order to estimate the quantity of light that is received by an homogeneous tissue when emitted by an optic fiber. A variance reduction method is studied and implemented, as well as a Markov chain Monte Carlo method based on the Metropolis-Hastings algorithm. The resulting estimating methods are then compared to the so-called Wang-Prahl (or Wang) method. Finally, the formal representation allows to derive a non-linear optimization algorithm close to Levenberg-Marquardt that is used for the estimation of the scattering and absorption coefficients of the tissue from measurements

Semaine d'Etude Mathématiques et Entreprises 5 : Propriétés asymptotiques de processus à volatilité stochastique

Cet article est une synthèse de notre travail de recherche durant la cinquième SEME (Semaine d'Etudes pour les Mathématiques en Entreprise) à l'Ecole des Mines de Nancy. Durant cette semaine, nous avons étudié une alternative au modèle de Black-Scholes: le modèle GARCH(1,1). Ce modèle est suffisamment simple pour être implémenté sur un ordinateur de bureau classique, et suffisamment proche du modèle de Black-Scholes pour ne pas dérouter les personnes habituées à ce dernier. Dans un premier temps, nous passons en revue différents résultats connus pour le modèle GARCH. En particulier, nous montrons que, sous certaines hypothèses, et contrairement au modèle de Black-Scholes, dans le modèle GARCH la distribution des rendements est à queue épaisse, similaire à celle d'une loi de puissance. Ensuite, nous illustrons à l'aide de simulations le comportement asymptotique de la distribution des rendements et nous proposons une méthode pour estimer le paramètre de la loi de puissance associée. Enfin, nous nous intéressons au phénomène de volatility clustering et à la durée des périodes de forte volatilité

An explorative approach to understanding individual differences in driving performance and neurocognition in long-term benzodiazepine users

Objective: Previous research reported cognitive and psychomotor impairments in long‐term users of benzodiazepine receptor agonists (BZRAs). This article explores the role of acute intoxication and clinical complaints. Methods: Neurocognitive and on‐road driving performance of 19 long‐term (≥6 months) regular (≥twice weekly) BZRA users with estimated plasma concentrations, based on self‐reported use, exceeding the therapeutic threshold (CBZRA+), and 31 long‐term regular BZRA users below (CBZRA−), was compared to that of 76 controls. Results: BZRA users performed worse on tasks of response speed, processing speed, and sustained attention. Age, but not CBZRA or self‐reported clinical complaints, was a significant covariate. Road‐tracking performance was explained by CBZRA only. The CBZRA + group exhibited increased mean standard deviation of lateral position comparable to that at blood‐alcohol concentrations of 0.5 g/L. Conclusions: Functional impairments in long‐term BZRA users are not attributable to self‐reported clinical complaints or estimated BZRA concentrations, except for road‐tracking, which was impaired in CBZRA + users. Limitations to address are the lack of assessment of objective clinical complaints, acute task related stress, and actual BZRA plasma concentrations. In conclusion, the results confirm previous findings that demonstrate inferior performance across several psychomotor and neurocognitive domains in long‐term BZRA users