Solving the time-dependent Schr\"odinger equation with absorbing boundary conditions and source terms in Mathematica 6.0

In recent decades a lot of research has been done on the numerical solution of the time-dependent Schr\"odinger equation. On the one hand, some of the proposed numerical methods do not need any kind of matrix inversion, but source terms cannot be easily implemented into this schemes; on the other, some methods involving matrix inversion can implement source terms in a natural way, but are not easy to implement into some computational software programs widely used by non-experts in programming (e.g. Mathematica). We present a simple method to solve the time-dependent Schr\"odinger equation by using a standard Crank-Nicholson method together with a Cayley's form for the finite-difference representation of evolution operator. Here, such standard numerical scheme has been simplified by inverting analytically the matrix of the evolution operator in position representation. The analytical inversion of the N x N matrix let us easily and fully implement the numerical method, with or without source terms, into Mathematica or even into any numerical computing language or computational software used for scientific computing.Comment: 15 pages, 7 figure

Three-body Interactions Improve the Prediction of Rate and Mechanism in Protein Folding Models

Here we study the effects of many-body interactions on rate and mechanism in protein folding, using the results of molecular dynamics simulations on numerous coarse-grained C-alpha-model single-domain proteins. After adding three-body interactions explicitly as a perturbation to a Go-like Hamiltonian with native pair-wise interactions only, we have found 1) a significantly increased correlation with experimental phi-values and folding rates, 2) a stronger correlation of folding rate with contact order, matching the experimental range in rates when the fraction of three-body energy in the native state is ~ 20%, and 3) a considerably larger amount of 3-body energy present in Chymotripsin inhibitor than other proteins studied.Comment: 9 pages, 2 tables and 5 figure

The merger of vertically offset quasi-geostrophic vortices

We examine the critical merging distance between two equal-volume, equal-potential-vorticity quasi-geostrophic vortices. We focus on how this distance depends on the vertical offset between the two vortices, each having a unit mean height-to-width aspect ratio. The vertical direction is special in the quasi-geostrophic model (used to capture the leading-order dynamical features of stably stratified and rapidly rotating geophysical flows) since vertical advection is absent. Nevertheless vortex merger may still occur by horizontal advection. In this paper, we first investigate the equilibrium states for the two vortices as a function of their vertical and horizontal separation. We examine their basic properties together with their linear stability. These findings are next compared to numerical simulations of the nonlinear evolution of two spheres of potential vorticity. Three different regimes of interaction are identified, depending on the vertical offset. For a small offset, the interaction differs little from the case when the two vortices are horizontally aligned. On the other hand, when the vertical offset is comparable to the mean vortex radius, strong interaction occurs for greater horizontal gaps than in the horizontally aligned case, and therefore at significantly greater full separation distances. This perhaps surprising result is consistent with the linear stability analysis and appears to be a consequence of the anisotropy of the quasi-geostrophic equations. Finally, for large vertical offsets, vortex merger results in the formation of a metastable tilted dumbbell vortex.Publisher PDFPeer reviewe

Folding of small proteins: A matter of geometry?

We review some of our recent results obtained within the scope of simple lattice models and Monte Carlo simulations that illustrate the role of native geometry in the folding kinetics of two state folders.Comment: To appear in Molecular Physic

The most effective but largely ignored target for prostate cancer early detection and intervention

Over the past two decades, the global efforts for the early detection and intervention of prostate cancer seem to have made significant progresses in the basic researches, but the clinic outcomes have been disappointing: (1) prostate cancer is still the most common non-cutaneous cancer in Europe in men, (2) the age-standardized prostate cancer rate has increased in nearly all Asian and African countries, (3) the proportion of advanced cancers at the diagnosis has increased to 8.2% from 3.9% in the USA, (4) the worldwide use of PSA testing and digital rectal examination have failed to reduce the prostate cancer mortality, and (5) there is still no effective preventive method to significantly reduce the development, invasion, and metastasis of prostate cancer… Together, these facts strongly suggest that the global efforts during the past appear to be not in a correlated target with markedly inconsistent basic research and clinic outcomes. The most likely cause for the inconsistence appears due to the fact that basic scientific studies are traditionally conducted on the cell lines and animal models, where it is impossible to completely reflect or replicate the in vivo status. Thus, we would like to propose the human prostate basal cell layer (PBCL) as “the most effective target for the early detection and intervention of prostate cancer”. Our proposal is based on the morphologic, immunohistochemical and molecular evidence from our recent studies of normal and cancerous human prostate tissues with detailed clinic follow-up data. We believe that the human tissue-derived basic research data may provide a more realistic roadmap to guide the clinic practice and to avoid the potential misleading from in vitro and animal studies

The 21Na(p,gamma)22Mg Reaction and Oxygen-Neon Novae

The 21Na(p,gamma)22Mg reaction is expected to play an important role in the nucleosynthesis of 22Na in Oxygen-Neon novae. The decay of 22Na leads to the emission of a characteristic 1.275 MeV gamma-ray line. This report provides the first direct measurement of the rate of this reaction using a radioactive 21Na beam, and discusses its astrophysical implications. The energy of the important state was measured to be E$_{c.m.}$= 205.7 $\pm$ 0.5 keV with a resonance strength $\omega\gamma = 1.03\pm0.16_{stat}\pm0.14_{sys}$ meV.Comment: Accepted for publication in Physical Review Letter

Reactivity of Biarylazacyclooctynones in Copper-Free Click Chemistry

The 1,3-dipolar cycloaddition of cyclooctynes with azides, also called "copper-free click chemistry", is a bioorthogonal reaction with widespread applications in biological discovery. The kinetics of this reaction are of paramount importance for studies of dynamic processes, particularly in living subjects. Here we performed a systematic analysis of the effects of strain and electronics on the reactivity of cyclooctynes with azides through both experimental measurements and computational studies using a density functional theory (DFT) distortion/interaction transition state model. In particular, we focused on biarylazacyclooctynone (BARAC) because it reacts with azides faster than any other reported cyclooctyne and its modular synthesis facilitated rapid access to analogues. We found that substituents on BARAC's aryl rings can alter the calculated transition state interaction energy of the cycloaddition through electronic effects or the calculated distortion energy through steric effects. Experimental data confirmed that electronic perturbation of BARAC's aryl rings has a modest effect on reaction rate, whereas steric hindrance in the transition state can significantly retard the reaction. Drawing on these results, we analyzed the relationship between alkyne bond angles, which we determined using X-ray crystallography, and reactivity, quantified by experimental second-order rate constants, for a range of cyclooctynes. Our results suggest a correlation between decreased alkyne bond angle and increased cyclooctyne reactivity. Finally, we obtained structural and computational data that revealed the relationship between the conformation of BARAC's central lactam and compound reactivity. Collectively, these results indicate that the distortion/interaction model combined with bond angle analysis will enable predictions of cyclooctyne reactivity and the rational design of new reagents for copper-free click chemistry