Can a microscopic stochastic model explain the emergence of pain cycles in patients?

A stochastic model is here introduced to investigate the molecular mechanisms which trigger the perception of pain. The action of analgesic drug compounds is discussed in a dynamical context, where the competition with inactive species is explicitly accounted for. Finite size effects inevitably perturb the mean-field dynamics: Oscillations in the amount of bound receptors spontaneously manifest, driven by the noise which is intrinsic to the system under scrutiny. These effects are investigated both numerically, via stochastic simulations and analytically, through a large-size expansion. The claim that our findings could provide a consistent interpretative framework to explain the emergence of cyclic behaviors in response to analgesic treatments, is substantiated.Comment: J. Stat. Mech. (Proceedings UPON2008

Non-Gaussian fluctuations in stochastic models with absorbing barriers

The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order corrections beyond the conventional Gaussian approximation. The theory is shown to successfully capture the non Gaussian traits of the sought distribution returning an excellent agreement with the simulations, for {\it all times} and arbitrarily {\it close} to the absorbing barrier. At large times, a compact analytical solution for the distribution of fluctuations is also obtained, bridging the gap with previous investigations, within the van Kampen picture and without resorting to alternative strategies, as elsewhere hypothesized.Comment: 2 figures, submitted to Phys. Rev. Let

Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions

A stochastic model of autocatalytic chemical reactions is studied both numerically and analytically. The van Kampen perturbative scheme is implemented, beyond the second order approximation, so to capture the non Gaussianity traits as displayed by the simulations. The method is targeted to the characterization of the third moments of the distribution of fluctuations, originating from a system of four populations in mutual interaction. The theory predictions agree well with the simulations, pointing to the validity of the van Kampen expansion beyond the conventional Gaussian solution.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

When does cyclic dominance lead to stable spiral waves?

Species diversity in ecosystems is often accompanied by characteristic spatio-temporal patterns. Here, we consider a generic two-dimensional population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species, mutation, pair-exchange and individual hopping. The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion. While the dynamics is generally characterized by spiraling patterns, we show that spiral waves are stable in only one of the four phases. Furthermore, we characterize a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn. Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiraling patterns are also affected by the nonlinear diffusion

A stochastic reaction scheme for drug/metabolite interaction

International audienceWe present a simplified stochastic model to investigate the mechanisms of action of tramadol, a centrally acting analgesic, used for treating pain. The model accounts for the process of metabolization through the cytochrome CYP2D6 and the interactions between molecules and target receptors. The proposed formulation is stochastic in nature and allows to speculate on the role of finite–size fluctuations. Analytically, the master equation, governing the process under scrutiny, is derived and studied in the mean–field limit. The analysis of the associated asymptotic behavior proves interesting for its potential medical implications. The analysis of fluctuations is carried on via the van Kampen expansion. Numerical simulations are also performed to confirm the adequacy of our theoretical prediction