Diffusion Dynamics, Moments, and Distribution of First Passage Time on the Protein-Folding Energy Landscape, with Applications to Single Molecules

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We obtain information for the first passage-time (FPT) distribution and its moments. The results show a dynamic transition temperature below which the FPT distribution develops a power-law tail, a signature of the intermittency phenomena of the folding dynamics. We also discuss the possible application of the results to single-molecule dynamics experiments

Orderly Spanning Trees with Applications

We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning tree, we provide an algorithm to compute an {\em orderly pair} for any connected planar graph $G$, consisting of a plane graph $H$ of $G$, and an orderly spanning tree of $H$. We also present several applications of orderly spanning trees: (1) a new constructive proof for Schnyder's Realizer Theorem, (2) the first area-optimal 2-visibility drawing of $G$, and (3) the best known encodings of $G$ with O(1)-time query support. All algorithms in this paper run in linear time.Comment: 25 pages, 7 figures, A preliminary version appeared in Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), Washington D.C., USA, January 7-9, 2001, pp. 506-51

VI-Band Follow-Up Observations of Ultra-Long-Period Cepheid Candidates in M31

The ultra-long period Cepheids (ULPCs) are classical Cepheids with pulsation periods exceeding $\approx 80$ days. The intrinsic brightness of ULPCs are ~1 to ~3 mag brighter than their shorter period counterparts. This makes them attractive in future distance scale work to derive distances beyond the limit set by the shorter period Cepheids. We have initiated a program to search for ULPCs in M31, using the single-band data taken from the Palomar Transient Factory, and identified eight possible candidates. In this work, we presented the VI-band follow-up observations of these eight candidates. Based on our VI-band light curves of these candidates and their locations in the color-magnitude diagram and the Period-Wesenheit diagram, we verify two candidates as being truly ULPCs. The six other candidates are most likely other kinds of long-period variables. With the two confirmed M31 ULPCs, we tested the applicability of ULPCs in distance scale work by deriving the distance modulus of M31. It was found to be $\mu_{M31,ULPC}=24.30\pm0.76$ mag. The large error in the derived distance modulus, together with the large intrinsic dispersion of the Period-Wesenheit (PW) relation and the small number of ULPCs in a given host galaxy, means that the question of the suitability of ULPCs as standard candles is still open. Further work is needed to enlarge the sample of calibrating ULPCs and reduce the intrinsic dispersion of the PW relation before re-considering ULPCs as suitable distance indicators.Comment: 13 pages, with 14 Figures and 4 Tables (one online table). AJ accepte

Effect of Na+ Flow on Cd2+ Block of Tetrodotoxin-resistant Na+ Channels

Tetrodotoxin-resistant (TTX-R) Na+ channels are 1,000-fold less sensitive to TTX than TTX-sensitive (TTX-S) Na+ channels. On the other hand, TTX-R channels are much more susceptible to external Cd2+ block than TTX-S channels. A cysteine (or serine) residue situated just next to the aspartate residue of the presumable selectivity filter “DEKA” ring of the TTX-R channel has been identified as the key ligand determining the binding affinity of both TTX and Cd2+. In this study we demonstrate that the binding affinity of Cd2+ to the TTX-R channels in neurons from dorsal root ganglia has little intrinsic voltage dependence, but is significantly influenced by the direction of Na+ current flow. In the presence of inward Na+ current, the apparent dissociation constant of Cd2+ (∼200 μM) is ∼9 times smaller than that in the presence of outward Na+ current. The Na+ flow–dependent binding affinity change of Cd2+ block is true no matter whether the direction of Na+ current is secured by asymmetrical chemical gradient (e.g., 150 mM Na+ vs. 150 mM Cs+ on different sides of the membrane, 0 mV) or by asymmetrical electrical gradient (e.g., 150 mM Na+ on both sides of the membrane, −20 mV vs. 20 mV). These findings suggest that Cd2+ is a pore blocker of TTX-R channels with its binding site located in a multiion, single-file region near the external pore mouth. Quantitative analysis of the flow dependence with the flux-coupling equation reveals that at least two Na+ ions coexist with the blocking Cd2+ ion in this pore region in the presence of 150 mM ambient Na+. Thus, the selectivity filter of the TTX-R Na+ channels in dorsal root ganglion neurons might be located in or close to a multiion single-file pore segment connected externally to a wide vestibule, a molecular feature probably shared by other voltage-gated cationic channels, such as some Ca2+ and K+ channels

Higher-order solutions to non-Markovian quantum dynamics via hierarchical functional derivative

Solving realistic quantum systems coupled to an environment is a challenging task. Here we develop a hierarchical functional derivative (HFD) approach for efficiently solving the non-Markovian quantum trajectories of an open quantum system embedded in a bosonic bath. An explicit expression for arbitrary order HFD equation is derived systematically. Moreover, it is found that for an analytically solvable model, this hierarchical equation naturally terminates at a given order and thus becomes exactly solvable. This HFD approach provides a systematic method to study the non-Markovian quantum dynamics of an open system coupled to a bosonic environment.Comment: 5 pages, 2 figure

Dynamical invariants in non-Markovian quantum state diffusion equation

We find dynamical invariants for open quantum systems described by the non-Markovian quantum state diffusion (QSD) equation. In stark contrast to closed systems where the dynamical invariant can be identical to the system density operator, these dynamical invariants no longer share the equation of motion for the density operator. Moreover, the invariants obtained with from bi-orthonormal basis can be used to render an exact solution to the QSD equation and the corresponding non-Markovian dynamics without using master equations or numerical simulations. Significantly we show that we can apply these dynamic invariants to reverse-engineering a Hamiltonian that is capable of driving the system to the target state, providing a novel way to design control strategy for open quantum systems.Comment: 6 pages, 2 figure