Neuromuscular excitability changes produced by sustained voluntary contraction and response to mexiletine in myotonia congenita

Objective: To investigate the cause of transient weakness in myotonia congenita (MC) and the mechanism of action of mexiletine in reducing weakness. Methods: The changes in neuromuscular excitability produced by 1. min of maximal voluntary contractions (MVC) were measured on the amplitude of compound muscle action potentials (CMAP) in two patients with either recessive or dominant MC, compared to control values obtained in 20 healthy subjects. Measurements were performed again in MC patients after mexiletine therapy. Results: Transient reduction in maximal CMAP amplitude lasting several minutes after MVC was evident in MC patients, whereas no change was observed in controls. Mexiletine efficiently reduced this transient CMAP depression in both patients. Discussion: Transient CMAP depression following sustained MVC may represent the electrophysiological correlate of the weakness clinically experienced by the patients. In MC, the low chloride conductance could induce self-sustaining action potentials after MVC, determining progressive membrane depolarization and a loss of excitability of muscle fibers, thus resulting in transient paresis. Mexiletine may prevent conduction block due to excessive membrane depolarization, thus reducing the transient CMAP depression following sustained MVC

Shell Model for Time-correlated Random Advection of Passive Scalars

We study a minimal shell model for the advection of a passive scalar by a Gaussian time correlated velocity field. The anomalous scaling properties of the white noise limit are studied analytically. The effect of the time correlations are investigated using perturbation theory around the white noise limit and non-perturbatively by numerical integration. The time correlation of the velocity field is seen to enhance the intermittency of the passive scalar.Comment: Replaced with final version + updated figure

On the canonically invariant calculation of Maslov indices

After a short review of various ways to calculate the Maslov index appearing in semiclassical Gutzwiller type trace formulae, we discuss a coordinate-independent and canonically invariant formulation recently proposed by A Sugita (2000, 2001). We give explicit formulae for its ingredients and test them numerically for periodic orbits in several Hamiltonian systems with mixed dynamics. We demonstrate how the Maslov indices and their ingredients can be useful in the classification of periodic orbits in complicated bifurcation scenarios, for instance in a novel sequence of seven orbits born out of a tangent bifurcation in the H\'enon-Heiles system.Comment: LaTeX, 13 figures, 3 tables, submitted to J. Phys.

Generally covariant state-dependent diffusion

Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non gauge-invariant systems is not unambiguously defined. They typically do not relax to equilibrium steady states even in the absence of extenal forces. Assuming both coordinate covariance and gauge invariance, we derive a second-order Langevin equation with state-dependent diffusion matrix and vanishing environmental forces. It differs from previous proposals but nevertheless entails the Einstein relation, a Maxwellian conditional steady state for the velocities, and the equipartition theorem. The over-damping limit leads to a stochastic differential equation in state space that cannot be interpreted as a pure differential (Ito, Stratonovich or else). At odds with the latter interpretations, the corresponding Fokker-Planck equation admits an equilibrium steady state; a detailed comparison with other theories of state-dependent diffusion is carried out. We propose this as a theory of diffusion in a heat bath with varying temperature. Besides equilibrium, a crucial experimental signature is the non-uniform steady spatial distribution.Comment: 24 page

Heat release by controlled continuous-time Markov jump processes

We derive the equations governing the protocols minimizing the heat released by a continuous-time Markov jump process on a one-dimensional countable state space during a transition between assigned initial and final probability distributions in a finite time horizon. In particular, we identify the hypotheses on the transition rates under which the optimal control strategy and the probability distribution of the Markov jump problem obey a system of differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh tends to zero, these equations converge to those satisfied by the diffusion process minimizing the heat released in the Langevin formulation of the same problem. We also show that in full analogy with the continuum case, heat minimization is equivalent to entropy production minimization. Thus, our results may be interpreted as a refined version of the second law of thermodynamics.Comment: final version, section 2.1 revised, 26 pages, 3 figure

Perturbations of Noise: The origins of Isothermal Flows

We make a detailed analysis of both phenomenological and analytic background for the "Brownian recoil principle" hypothesis (Phys. Rev. A 46, (1992), 4634). A corresponding theory of the isothermal Brownian motion of particle ensembles (Smoluchowski diffusion process approximation), gives account of the environmental recoil effects due to locally induced tiny heat flows. By means of local expectation values we elevate the individually negligible phenomena to a non-negligible (accumulated) recoil effect on the ensemble average. The main technical input is a consequent exploitation of the Hamilton-Jacobi equation as a natural substitute for the local momentum conservation law. Together with the continuity equation (alternatively, Fokker-Planck), it forms a closed system of partial differential equations which uniquely determines an associated Markovian diffusion process. The third Newton law in the mean is utilised to generate diffusion-type processes which are either anomalous (enhanced), or generically non-dispersive.Comment: Latex fil

Painful and painless mutations of SCN9A and SCN11A voltage-gated sodium channels

Chronic pain is a global problem affecting up to 20% of the world’s population and has a significant economic, social and personal cost to society. Sensory neurons of the dorsal root ganglia (DRG) detect noxious stimuli and transmit this sensory information to regions of the central nervous system (CNS) where activity is perceived as pain. DRG neurons express multiple voltage-gated sodium channels that underlie their excitability. Research over the last 20 years has provided valuable insights into the critical roles that two channels, NaV1.7 and NaV1.9, play in pain signalling in man. Gain of function mutations in NaV1.7 cause painful conditions while loss of function mutations cause complete insensitivity to pain. Only gain of function mutations have been reported for NaV1.9. However, while most NaV1.9 mutations lead to painful conditions, a few are reported to cause insensitivity to pain. The critical roles these channels play in pain along with their low expression in the CNS and heart muscle suggest they are valid targets for novel analgesic drugs