On the superfluidity of classical liquid in nanotubes

In 2001, the author proposed the ultra second quantization method. The ultra second quantization of the Schr\"odinger equation, as well as its ordinary second quantization, is a representation of the N-particle Schr\"odinger equation, and this means that basically the ultra second quantization of the equation is the same as the original N-particle equation: they coincide in 3N-dimensional space. We consider a short action pairwise potential V(x_i -x_j). This means that as the number of particles tends to infinity, $N\to\infty$, interaction is possible for only a finite number of particles. Therefore, the potential depends on N in the following way: $V_N=V((x_i-x_j)N^{1/3})$. If V(y) is finite with support $\Omega_V$, then as $N\to\infty$ the support engulfs a finite number of particles, and this number does not depend on N. As a result, it turns out that the superfluidity occurs for velocities less than $\min(\lambda_{\text{crit}}, \frac{h}{2mR})$, where $\lambda_{\text{crit}}$ is the critical Landau velocity and R is the radius of the nanotube.Comment: Latex, 20p. The text is presented for the International Workshop "Idempotent and tropical mathematics and problems of mathematical physics", Independent University of Moscow, Moscow, August 25--30, 2007 and to be published in the Russian Journal of Mathematical Physics, 2007, vol. 15, #

Conformational rearrangements in the transmembrane domain of CNGA1 channels revealed by single-molecule force spectroscopy

Cyclic nucleotide-gated (CNG) channels are activated by binding of cyclic nucleotides. Although structural studies have identified the channel pore and selectivity filter, conformation changes associated with gating remain poorly understood. Here we combine single-molecule force spectroscopy (SMFS) with mutagenesis, bioinformatics and electrophysiology to study conformational changes associated with gating. By expressing functional channels with SMFS fingerprints in Xenopus laevis oocytes, we were able to investigate gating of CNGA1 in a physiological-like membrane. Force spectra determined that the S4 transmembrane domain is mechanically coupled to S5 in the closed state, but S3 in the open state. We also show there are multiple pathways for the unfolding of the transmembrane domains, probably caused by a different degree of \u3b1-helix folding. This approach demonstrates that CNG transmembrane domains have dynamic structure and establishes SMFS as a tool for probing conformational change in ion channels