Theory of diatomic molecules in an external electromagnetic field from first quantum mechanical principles

We study a general problem of the translational/rotational/vibrational/electronic dynamics of a diatomic molecule exposed to an interaction with an arbitrary external electromagnetic field. The theory developed in this paper is relevant to a variety of specific applications. Such as, alignment or orientation of molecules by lasers, trapping of ultracold molecules in optical traps, molecular optics and interferometry, rovibrational spectroscopy of molecules in the presence of intense laser light, or generation of high order harmonics from molecules. Starting from the first quantum mechanical principles, we derive an appropriate molecular Hamiltonian suitable for description of the center of mass, rotational, vibrational and electronic molecular motions driven by the field within the electric dipole approximation. Consequently, the concept of the Born-Oppenheimer separation between the electronic and the nuclear degrees of freedom in the presence of an electromagnetic field is introduced. Special cases of the dc/ac field limits are then discussed separately. Finally, we consider a perturbative regime of a weak dc/ac field, and obtain simple analytic formulas for the associated Born-Oppenheimer translational/rotational/vibrational molecular Hamiltonian

Comparison of RNA localization during oogenesis within Acipenser ruthenus and Xenopus laevis

The oocyte is a unique cell, from which develops a complex organism comprising of germ layers, tissues and organs. In some vertebrate species it is known that the asymmetrical localization of biomolecules within the oocyte is what drives the spatial differentiation of the daughter cells required for embryogenesis. This asymmetry is first established to produce an animal-vegetal (A-V) axis which reflects the future specification of the ectoderm, mesoderm, and endoderm layers. Several pathways for localization of vegetal maternal transcripts have already been described using a few animal models. However, there is limited information about transcripts that are localized to the animal pole, even though there is accumulating evidence indicating its active establishment. Here, we performed comparative TOMO-Seq analysis on two holoblastic cleavage models: Xenopus laevis and Acipenser ruthenus oocytes during oogenesis. We found that there were many transcripts that have a temporal preference for the establishment of localization. In both models, we observed vegetal transcript gradients that were established during either the early or late oogenesis stages and transcripts that started their localization during the early stages but became more pronounced during the later stages. We found that some animal gradients were already established during the early stages, however the majority were formed during the later stages of oogenesis. Some of these temporally localized transcripts were conserved between the models, while others were species specific. Additionally, temporal de novo transcription and also degradation of transcripts within the oocyte were observed, pointing to an active remodeling of the maternal RNA pool

Intracellular expression profiles measured by real-time PCR tomography in the Xenopus laevis oocyte

Real-time PCR tomography is a novel, quantitative method for measuring localized RNA expression profiles within single cells. We demonstrate its usefulness by dissecting an oocyte from Xenopus laevis into slices along its animal–vegetal axis, extracting its RNA and measuring the levels of 18 selected mRNAs by real-time RT-PCR. This identified two classes of mRNA, one preferentially located towards the animal, the other towards the vegetal pole. mRNAs within each group show comparable intracellular gradients, suggesting they are produced by similar mechanisms. The polarization is substantial, though not extreme, with around 5% of vegetal gene mRNA molecules detected at the animal pole, and around 50% of the molecules in the far most vegetal section. Most animal pole mRNAs were found in the second section from the animal pole and in the central section, which is where the nucleus is located. mRNA expression profiles did not change following in vitro fertilization and we conclude that the cortical rotation that follows fertilization has no detectable effect on intracellular mRNA gradients

Mathematical Analysis of Copy Number Variation in a DNA Sample Using Digital PCR on a Nanofluidic Device

Copy Number Variations (CNVs) of regions of the human genome have been associated with multiple diseases. We present an algorithm which is mathematically sound and computationally efficient to accurately analyze CNV in a DNA sample utilizing a nanofluidic device, known as the digital array. This numerical algorithm is utilized to compute copy number variation and the associated statistical confidence interval and is based on results from probability theory and statistics. We also provide formulas which can be used as close approximations

Studying copy number variations using a nanofluidic platform

Copy number variations (CNVs) in the human genome are conventionally detected using high-throughput scanning technologies, such as comparative genomic hybridization and high-density single nucleotide polymorphism (SNP) microarrays, or relatively low-throughput techniques, such as quantitative polymerase chain reaction (PCR). All these approaches are limited in resolution and can at best distinguish a twofold (or 50%) difference in copy number. We have developed a new technology to study copy numbers using a platform known as the digital array, a nanofluidic biochip capable of accurately quantitating genes of interest in DNA samples. We have evaluated the digital array's performance using a model system, to show that this technology is exquisitely sensitive, capable of differentiating as little as a 15% difference in gene copy number (or between 6 and 7 copies of a target gene). We have also analyzed commercial DNA samples for their CYP2D6 copy numbers and confirmed that our results were consistent with those obtained independently using conventional techniques. In a screening experiment with breast cancer and normal DNA samples, the ERBB2 gene was found to be amplified in about 35% of breast cancer samples. The use of the digital array enables accurate measurement of gene copy numbers and is of significant value in CNV studies

The effect of polarization on the light-induced conical intersection phenomenon

It has already been shown that dressing of diatomic molecules by standing or running linear polarized laser waves gives rise to conical intersections (CIs). Due to the presence of such CIs, the rovibronic molecular motions are strongly coupled. Here we prove that only perfect linear polarized light induces CIs in diatomic molecules. However, the fingerprints of the light-induced conical intersection survive for an elliptical polarization but not for a circular polarization. Therefore, the effects of the light-induced conical intersection can be controlled by varying a physical parameter (polarization of the laser). Such a CI controllable physical parameter does not exist in field-free polyatomic molecules. An illustrative numerical example for a sodium dimer showing the dependence of the absorption spectrum of Na(2) upon ellipticity is given