Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field

We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide us with a straightforward possibility to consider formation of anomalous stationary states and superdiffusion processes, both properties are inherent to strongly non-equilibrium plasmas of solar systems and thermonuclear devices. We solve fractional kinetic equations, study the properties of the solution, and compare analytical results with those of numerical simulation based on the solution of the Langevin equations with the noise source having Levy stable probability density. We found, in particular, that the stationary states are essentially non-Maxwellian ones and, at the diffusion stage of relaxation, the characteristic displacement of a particle grows superdiffusively with time and is inversely proportional to the magnetic field.Comment: 15 pages, LaTeX, 5 figures PostScrip

Fractional transport equations for Levy stable processes

The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a Brownian system subjected to a Levy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limit of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the fractional character acquired by the position in the Smoluchowski equation follows from the fractional character of the momentum in the Klein-Kramers equation. Connections among fractional transport equations recently proposed are clarified.Comment: 4 page

Linear Relaxation Processes Governed by Fractional Symmetric Kinetic Equations

We get fractional symmetric Fokker - Planck and Einstein - Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known kinetic equations of the Brownian motion theory and contain symmetric fractional derivatives over velocity and space, respectively. With the help of these equations we study analytically the processes of linear relaxation in a force - free case and for linear oscillator. For a weakly damped oscillator we also get kinetic equation for the distribution in slow variables. Linear relaxation processes are also studied numerically by solving corresponding Langevin equations with the source which is a discrete - time approximation to a white Levy noise. Numerical and analytical results agree quantitatively.Comment: 30 pages, LaTeX, 13 figures PostScrip

Pharmacological Characterization of Human m1 Muscarinic Acetylcholine Receptors with Double Mutations at the Junction of TM VI and the Third Extracellular Domain 1

ABSTRACT A mutant human m5 receptor containing the mutations of Ser465 to Tyr and Thr466 to Pro showed constitutive activity. By replacing the equivalent Ser388 with Tyr and Thr389 with Pro, we created a mutant human m1 (Hm1) receptor with comparable double mutations. The mutant receptor, Hm1(Ser388Tyr, Thr389Pro), was stably expressed in A9 L cells and displayed enhanced responses to classical muscarinic agonists with significantly increased potencies. Choline, a normal component of growth media, showed an efficacy comparable to acetylcholine and carbachol at Hm1(Ser388Tyr, Thr389Pro) receptors. Methylcarbachol, a selective nicotinic agonist, exhibited partial agonist activity at human m1 wild-type receptors and full agonist activity at Hm1(Ser388Tyr, Thr389Pro) receptors. l-Hyoscyamine inhibited the activities of choline and methylcarbachol. Muscarinic antagonists displayed small reductions in binding affinities, although muscarinic agonists showed greatly increased binding affinities for Hm1(Ser388Tyr, Thr389Pro) receptors. All agonists, including choline and methylcarbachol, showed multiple affinity states at Hm1(Ser388Tyr, Thr389Pro) receptors in the absence of GppNHp. The high affinity binding sites for acetylcholine, arecoline and choline were shifted in the presence of GppNHp. These results suggest that Hm1(Ser388Tyr, Thr389Pro) is conformationally favorable for agonist binding and receptor activation. Muscarinic acetylcholine receptors are members of the large family of G protein-coupled receptors mediating signal transduction and represent important targets for drug design and development. Five subtypes of muscarinic receptors, named m1 to m5, have been cloned. Functionally, they can be classified into two groups, the m1, m3 and m5 subtypes are preferentially coupled to the activation of phospholipase C ␤ through the pertussis toxin-insensitive G q/11 family of G proteins; while the m2 and m4 subtypes are mainly coupled to the inhibition of adenylyl cyclase through the pertussis toxinsensitive G i family of G proteins. Previous molecular modelling studies A mutant Hm5 receptor with Ser465 and Thr466 at the junction of TM VI and the N-terminal of the third extracellular domain (Ne3) mutated to Tyr and Pro, respectively, ABBREVIATIONS: ACh, acetylcholine; APE, arecaidine propargyl ester hydrobromide, DMEM, Dulbecco's Modified Eagle Media; FBS, fetal bovine serum; GppNHp, guanylylimidodiphosphate; Hm1, human muscarinic acetylcholine receptor subtype 1; Hm1(Ser388Tyr, Thr389Pro), Hm1 mutant receptor with the mutations of Ser388 to Tyr and Thr389 to Pro; Hm5, human muscarinic acetylcholine receptor subtype 5; IP, inositol phosphate; KH buffer, Krebs-Henseleit buffer, mAChR, muscarinic acetylcholine receptor; (R)-QNB, (R)-3-quinuclidinyl benzilate; Ne3, N-terminal region of the third extracellular domain; TCA, trichloroacetic acid, TM, transmembrane domain; WT, wild-type; KSHV-GPCR, G-protein-coupled receptor of Kaposi's sarcoma-associated herpesvirus