An optimized semiclassical approximation for vibrational response functions.

The observables of multidimensional infrared spectroscopy may be calculated from nonlinear vibrational response functions. Fully quantum dynamical calculations of vibrational response functions are generally impractical, while completely classical calculations are qualitatively incorrect at long times. These challenges motivate the development of semiclassical approximations to quantum mechanics, which use classical mechanical information to reconstruct quantum effects. The mean-trajectory (MT) approximation is a semiclassical approach to quantum vibrational response functions employing classical trajectories linked by deterministic transitions representing the effects of the radiation-matter interaction. Previous application of the MT approximation to the third-order response function R(3)(t3, t2, t1) demonstrated that the method quantitatively describes the coherence dynamics of the t3 and t1 evolution times, but is qualitatively incorrect for the waiting-time t2 period. Here we develop an optimized version of the MT approximation by elucidating the connection between this semiclassical approach and the double-sided Feynman diagrams (2FD) that represent the quantum response. Establishing the direct connection between 2FD and semiclassical paths motivates a systematic derivation of an optimized MT approximation (OMT). The OMT uses classical mechanical inputs to accurately reproduce quantum dynamics associated with all three propagation times of the third-order vibrational response function.

Comparative epigenomics of human and mouse mammary tumors.

Gene silencing by aberrant epigenetic chromatin alteration is a well-recognized event contributing to tumorigenesis. Although genetically engineered tumor-prone mouse models have proven a powerful tool in understanding many aspects of carcinogenesis, to date few studies have focused on epigenetic alterations in mouse tumors. To uncover epigenetically silenced tumor suppressor genes (TSGs) in mouse mammary tumor cells, we conducted initial genome-wide screening by combining the treatment of cultured cells with the DNA demethylating drug 5-aza-2'-deoxycytidine (5-azadC) and the histone deacetylase inhibitor trichostatin A (TSA) with expression microarray. By conducting this initial screen on EMT6 cells and applying protein function and genomic structure criteria to genes identified as upregulated in response to 5-azadC/TSA, we were able to identify two characterized breast cancer TSGs (Timp3 and Rprm) and four putative TSGs (Atp1B2, Dusp2, FoxJ1 and Smpd3) silenced in this line. By testing a panel of 10 mouse mammary tumor lines, we determined that each of these genes is commonly hypermethylated, albeit with varying frequency. Furthermore, by examining a panel of human breast tumor lines and primary tumors we observed that the human orthologs of ATP1B2, FOXJ1 and SMPD3 are aberrantly hypermethylated in the human disease whereas DUSP2 was not hypermethylated in primary breast tumors. Finally, we examined hypermethylation of several genes targeted for epigenetic silencing in human breast tumors in our panel of 10 mouse mammary tumor lines. We observed that the orthologs of Cdh1, RarB, Gstp1, RassF1 genes were hypermethylated, whereas neither Dapk1 nor Wif1 were aberrantly methylated in this panel of mouse tumor lines. From this study, we conclude that there is significant, but not absolute, overlap in the epigenome of human and mouse mammary tumors.

Two-dimensional spectroscopy of coupled vibrations with the optimized mean-trajectory approximation.

The optimized mean-trajectory (OMT) approximation is a semiclassical representation of the nonlinear vibrational response function used to compute multidimensional infrared spectra. In this method, response functions are calculated from a sequence of classical trajectories linked by discontinuities representing the effects of radiation-matter interactions, thus providing an approximation to quantum dynamics using classical inputs. This approach was previously formulated and assessed numerically for a single anharmonic degree of freedom. Our previous work is generalized here in two respects. First, the derivation of the OMT is extended to any number of coupled anharmonic vibrations by determining semiclassical approximations for pairs of double-sided Feynman diagrams. Second, an efficient numerical procedure is developed for calculating two-dimensional infrared spectra of coupled anharmonic vibrations in the OMT approximation. The OMT approximation is shown to reproduce the fundamental features of the quantum response function including both coherence and population dynamics.