Principles of rapid polymerase chain reactions: mathematical modeling and experimental verification

Polymerase chain reaction (PCR) is an important diagnostic tool for the amplification of DNA. The PCR process can be treated as a problem in biochemical engineering. This study focuses on the development of a mathematical model of the polymerase chain reaction. The PCR process consists of three steps: denaturation of target DNA, annealing of sequence-specific oligonucleotide primers and the enzyme-catalyzed elongation of the annealed complex (primer:DNA:polymerase). The denaturation step separates the double strands of DNA; this model assumes denaturation is complete. The annealing step describes the formation of a primer-fragment complex followed by the attachment of the polymerase to form a ternary complex. This step is complicated by competitive annealing between primers and incomplete fragments including primer-primer reactions. The elongation step is modeled by a stochastic method. Species that compete during the elongation step are deoxynucleotide triphosphates dCTP, dATP, dTTP, dGTP, dUTP, and pyrophosphate. Thermal deamination of dCTP to form dUTP is included in the model. The probability for a species to arrive at the active site is based on its molar fraction. The number of random insertion events depends on the average processing speed of the polymerase and the elongation time of the simulation. The numerical stochastic experiment is repeated a sufficient number of times to construct a probability density distribution (PDF). The moment of the PDF and the annealing step products provide the product distribution at the end of the elongation step. The overall yield is compared to six experimental values of the yield. In all cases the comparisons are very good.     

The absolute sign of J coupling constants determined using the order matrix calculation

A novel methodology using the order matrix calculation to determine the absolute sign of spin-spin couplings based on the structure of organic compounds is presented. The sign of the residual dipolar coupling (RDC) depends on the sign of corresponding scalar spin-spin coupling constant and the sign of the RDC has a dramatic influence on the order matrix calculation. Therefore, the sign of the spin-spin coupling constant can be obtained by an order matrix calculation through the corresponding RDC. Six types of spin-spin coupling constants, including 2J(H,H), 1J(C,F), 2J(C,F), 3J(C,F), 2J(F,H) and 3J(F,H), were obtained simultaneously. Except for 3J(C,F) where the measured RDCs have very small magnitudes, the signs were determined unambiguously.     

Location of type B carbonate ion in type A-B carbonate apatite synthesized at high pressure

The structure of a complex, disordered type A-B carbonate apatite (CAp) of approximate composition Ca₁₀(PO₄)_6−y(CO₃)_x+(3/2)y(OH)_2−2x, x-0.7, y-0.6, synthesized at 3 GPa, 1400°C has been determined using single-crystal X-ray diffraction and FTIR spectroscopy at room temperature and pressure. Crystal data are: hexagonal, space group P6₃/m, Z=1; a=9.5143(3), c=6.8821(2) Å, V=539.5 Å³, and R=0.025. There are three structural locations for the carbonate ion. The channel carbonate is mainly in the closed vertical configuration of the structure, with two of its oxygen atoms close to the c-axis (A1 carbonate; IR bands at 1541 and 1449 cm⁻¹), but subordinate amounts are also located in an open vertical configuration (A2 carbonate; IR bands at 1563 and 1506 cm⁻¹). The type B carbonate ion is located close to the sloping faces of the PO₄ tetrahedron (IR bands at 1474 and 1406 cm⁻¹), confirming earlier inferences from polarized IR spectra.     

The inclusion of electrostatic hydration energies in molecular mechanics calculations

Summary The problem of including solvent effects in molecular mechanics calculations is discussed. It is argued that the neglect of charge-solvent (solvation) interactions can introduce significant errors. The finite difference Poisson-Boltzmann (FDPB) method for calculating electrostatic interactions is summarized and is used as a basis for introducing a new pairwise energy term which accounts for charge-solvent interactions. This term acts between all pairs of atoms usually considered in molecular mechanics calculations and can be easily incorporated into existing force fields. As an example, a parameterization is developed for the CHARMm force field and the results compared to the predictions of the FDPB method. An approach to the realistic incorporation of solvent screening into force fields is also outlined.     

The Adamantane Rearrangement of 1,2endo-Trimethylenenorbornane. Preliminary communication

1,2endo-Trimethylenenorbornane (1) in the presence of aluminium bromide in carbon disulfide at ?60° isomerizes at a much higher rate than its 2exo-isomer 2 to 2endo, 6endo-trimethylenenorbornane (3) as the sole product. By consequence, the hydrocarbon 2 being the next intermediate in the sequence of the adamantane rearrangement of 1 seems to be very unlikely.     

Cyclopropane chemistry. Part 5 [1,2]. Hexafluorocyclopropane as a source of difluorocarbene

Thermolysis of hexafluorocyclopropane in the presence of ethylene, propene, vinyl chloride, and vinyl bromide gives good yields of the corresponding 1,1-difluorocyclopropanes, formed by addition of difluorocarbene to the olefin. The tetrafluoroethylene formed dimerises to octafluorocyclobutane, co-dimerises with the olefin, or survives, depending on the reaction conditions. With allene, hexafluorocyclopropane gives 1-(difluoromethylene)cyclopropane, 2,2,3,3-tetrafluorospiropentane, and products derived from tetrafluoroethylene and allene.     

Synthesis and Characterization of Three Homoleptic Bismuth Silanolates: [Bi(OSiR3)3] (R = Me,Et, iPr)

The bismuth tris(triorganosilanolates) [Bi(OSiR₃)₃] ( 1 , R = Me; 2 , R = Et; 3 , R = iPr) were prepared by reaction of R₃SiOH with [Bi(OtBu)₃]. Compound 1 crystallizes in the triclinic space group with Z = 2 and the lattice constants a = 10.323(1) Å, b = 13.805(1) Å, c = 21.096(1) Å and α = 91.871(4)°, β = 94.639(3)°, γ = 110.802(3)°. In the solid state compound 1 is a trimer as result of weak intermolecular bismuth‐oxygen interactions with Bi–O distances in the range 2.686(6)–3.227(3) Å. The coordination at the bismuth atoms Bi(1) and Bi(3) is best described as 3 + 2 coordination whereas Bi(2) shows a 3 + 3 coordination. The intramolecular Bi–O distances fall in the range 2.041(3)–2.119(3) Å. Compound 3 crystallizes in the orthorhombic space group Pbcm with Z = 4 and the lattice constants a = 7.201(1) Å, b = 23.367(5) Å and c = 20.893(1) Å, whereas the triethylsilyl‐derivative 2 is liquid. In contrast to [Bi(OSiMe₃)₃] ( 1 ) compound 3 is monomeric in the solid state, but shows similar intramolecular Bi–O distances in the range 1.998(2)–2.065(5) Å. The bismuth silanolates are highly soluble in common organic solvents and strongly moisture sensitive. Compound 1 shows the lowest thermal stability.     

Optical spectroscopy of RuC: 18,000-24,000 cm(-1)

The optical spectrum of diatomic RuC has been recorded from 17 800 to 24 200 cm(-1). Three previously unidentified excited electronic states were analyzed and identified as having Omega' = 0, Omega' = 2, and Omega' = 3. The Omega' = 3 state was determined to be a 3Delta3 state that is suggested to arise from a mixture of the 10sigma(2)11sigma(2)5pi(3)2delta(3)12sigma(1)6pi(1) and 10sigma(2)11sigma(1)5pi(3)2delta(3)12sigma(2)6pi(1) electronic configurations. Three additional bands belonging to the previously observed [18.1] (1)Pi<--X (1)Sigma(+) system were analyzed to obtain B(e) (')=0.558 244(48) cm(-1), alpha(e) (')=0.004 655(27) cm(-1), omegae' = 887.201(37) cm(-1), and omega(e) 'xe' = 5.589(7) cm(-1) for the 102Ru 12C isotopomer (1sigma error limits). A Rydberg-Klein-Rees analysis was then performed using the determined spectroscopic constants of the [18.1] 1Pi state, and similar analyses were performed for the previously observed states. The resulting potential energy curves are provided for the 100Ru 12C, 101Ru 12C, 102Ru 12C, and 104Ru 12C isotopic species.     

Tilt of atomic force microscope cantilevers: effect on spring constant and adhesion measurements

In atomic force microscopy, the cantilevers are mounted under a certain tilt angle alpha with respect to the sample surface. In this paper, we show that this increases the effective spring constant by typically 10-20%. The effective spring constant of a rectangular cantilever of length L can be obtained by dividing the measured spring constant by cos2 alpha(1 - 2D tan alpha/L). Here, alpha is the tilt angle and D is the size of the tip. In colloidal probe experiments, D has to be replaced by the radius of the attached particle. To determine the effect of tilt experimentally, the adhesion force between spherical borosilicate particles and planar silicon oxide surfaces was measured at tilt angles between 0 degrees and 35 degrees. The experiments revealed a significant decrease of the mean apparent adhesion force with a tilt of typically 20-30% at alpha = 20 degrees. In addition, they demonstrate that the adhesion depends drastically on the precise position of contact on the particle surface.