Single-molecule measurements of trapped and migrating circular DNA during electrophoresis in agarose gels

The effect of agarose gel concentration and field strength on the electrophoretic trapping of open (relaxed) circular DNA was investigated using microscopic measurements of individual molecules stained with a fluorescent dye. Three open circles with sizes of 52.5, 115, and 220 kbp were trapped by the electric field (6 V/cm) and found to be predominately fixed and stretched at a single point in the gel. The length of the stretched circles did not significantly change with agarose concentration of the gels (mass fractions of 0.0025, 0.01, and 0.02). The relaxation kinetics of the trapped circles was also measured in the gels. The relaxation of the large open circles was found to be a slow process, taking several seconds. The velocity and average length of the 52.5 kbp open circles and 48.5 kbp linear DNA were measured during electrophoresis in the agarose gels. The velocity increased when the agarose concentrations were lowered, but the average length of the open-circle DNA (during electrophoresis) did not significantly change with agarose gel concentrations. The circles move through the gels by cycles of stretching and relaxation during electrophoresis. Linear dichroism was also used to investigate the trapping and alignment of the 52.5 kbp open circles. The results in this study provide information that can be used to improve electrophoretic separations of circular DNA, an important form of genetic material and commonly used to clone DNA.     

Investigation of the electronic structure of the BiSBr and BiSeBr clusters by density functional method

The energy levels of valence bands (VB) of the BiSBr and BiSeBr crystals have been calculated for investigation of the photoelectron emission spectra of BiSBr, BiSeBr and BiSI crystals. The molecular model of this crystal has been used for the calculation of VB by the Density Functional Theory (DFT) method. The molecular cluster, consisting of 20 molecules of BiSBr, BiSeBr, has been used for calculations of averaged total density of states, including atom vibrations. The spectra of the averaged total density of states from VB of BiSBr and BiSeBr clusters have been compared with the experimental photoelectron emission spectra from VB of BiSI crystals. The results clarify that the atomic vibrations in A⁵B⁶C⁷ type crystals with chain structure create a smoother appearance of the averaged total density of state spectrum and the experimental X-ray photoemission spectra (XPS).     

Askey-Wilson relations and Leonard pairs

It is known that if (A,A^*) is a Leonard pair, then the linear transformations A, A^* satisfy the Askey-Wilson relations

     

A multistate model for the fluorescence response of R-phycoerythrin

Although strong fluorescence makes the R-phycoerythrin (R-PE) proteins increasingly useful in biological and clinical assays, they are subject to nonlinear effects including transitions to collective dark states and photodegradation, which complicate quantitative applications. We report measurements of R-PE fluorescence intensity as a function of incident power, duration of illumination and temperature. Emission intensity in the band at 570 nm is proportional to incident power for low power levels. At higher incident power, the emission at 570 nm is smaller than expected from a linear dependence on power. We propose that R-PE undergoes both reversible emission cessation on a millisecond time scale attributed to transitions to a collective dark state, and irreversible photodegradation on a time scale of minutes. Singlet oxygen scavengers such as dithiothreitol and n-propyl gallate have protective effects against the latter effect but not the former. Electrophoretic analysis of irradiated solutions of R-PE indicates that significant noncovalent aggregation is correlated with photodegradation. A multistate model based on fluorescence measurements and geometric analysis is proposed for the fluorophores in R-PE. The phycobilin fluorophores are partitioned into three groups: the phycourobilins (PUB) absorbing at 490 nm, one group of phycoerythobilins (PEB) absorbing at 530 nm (PEB-530) and another group of PEB absorbing at 560 nm (PEB-560). The two processes that result in the loss of fluorescence intensity are most likely associated with the PEB-560 group.     

Investigation of the electronic structure of the SbSeBr cluster

The energy levels of valence bands (VB) in SbSeBr crystals were calculated for investigation of the photoelectron emission spectra of A⁵B⁶C⁷ — type crystals. The molecular model of this crystal was used for calculation of VB by the Density Functional Theory (DFT) and Unrestricted Hartree — Fock (UHF) methods. The molecular cluster consisting of 20 molecules of SbSeBr was used for calculations of averaged total density of states including atom vibrations. The spectra of averaged total density of states from VB in the SbSeBr cluster were compared with experimental photoelectron emission spectra from VB of A⁵B⁶C⁷ — type crystals. The results of comparison clarify that the atomic vibrations are one of possible reasons for the smoother appearance of the experimental X-ray photoelectron spectrum (XPS).      

A Poisson bridge between fractional Brownian motion and stable Lévy motion

We study a non-Gaussian and non-stable process arising as the limit of sums of rescaled renewal processes under the condition of intermediate growth. The process has been characterized earlier by the cumulant generating function of its finite-dimensional distributions. Here, we derive a more tractable representation for it as a stochastic integral of a deterministic function with respect to a compensated Poisson random measure. Employing the representation we show that the process is locally and globally asymptotically self-similar with fractional Brownian motion and stable Lévy motion as its tangent limits.     

A generalization of Clausen’s identity

The paper gives an extension of Clausen’s identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related third-order linear differential equation are found in terms of certain bivariate series that can reduce to ₃F₂ series similar to those in Clausen’s identity. The general contiguous variation of Clausen’s identity is found as well. The related Chaundy’s identity is generalized without any restriction on the parameters of the Gauss hypergeometric function. The special case of dihedral Gauss hypergeometric functions is underscored.