Quantum Mechnical Investion of Cyclic 3',5'- Adenosine Monophosphate, the Second Hormonal Messenger

Full geometry optimizations using the PM3, AM1, 3-21G∗/HF and 6-31G∗/HF levels of theory were conducted on the syn and anti conformations of cyclic3′,5′-adenosine monophosphate (cAMP). Comparison of the anti crystal structures with the semiempirical and ab initio results revealed that the ab initio results agree well with the experimental results. The results of semiempirical calculations are in qualitative agreement with experimental and ab initio values, with the exception of the glycosyl torsion angle for the anti conformer. Sugar puckering, which is not handled properly by semiempirical methods for unconstrained sugars, nucleosides, nucleotides and nucleotide base pairs, is modeled reasonably well by the semiempirical methods for cAMP. This improvement results from the constraints introduced by the cyclization of AMP to form the phosphodiester.

Hydrogen bonding of nucleotide base pairs: Application of the PM3 method

The ability of the pm3 semiempirical quantum mechanical method to reproduce hydrogen bonding in nucleotide base pairs was assessed. Results of pm3 calculations on the nucleotides 2′-deoxyadenosine 5′-monophosphate (pdA), 2′-deoxyguanosine 5′-monophosphate (pdG), 2′-deoxycytidine 5′-monophosphate (pdC), and 2′-deoxythymidine 5′-monophosphate (pdT) and the base pairs pdA–pdT, pdG–pdC, and pdG(syn)–pdC are presented and discussed. The pm3 method is the first of the parameterized nddo quantum mechanical models with any ability to reproduce hydrogen bonding between nucleotide base pairs. Intermolecular hydrogen bond lengths between nucleotides displaying Watson–Crick base pairing are 0.1–0.2 Å less than experimental results. Nucleotide bond distances, bond angles, and torsion angles about the glycosyl bond (χ), the C4′C5′ bond (γ), and the C5′O5′ bond (β) agree with experimental results. There are many possible conformations of nucleotides. pm3 calculations reveal that many of the most stable conformations are stabilized by intramolecular CHO hydrogen bonds. These interactions disrupt the usual sugar puckering. The stacking interactions of a dT–pdA duplex are examined at different levels of gradient optimization. The intramolecular hydrogen bonds found in the nucleotide base pairs disappear in the duplex, as a result of the additional constraints on the phosphate group when part of a DNA backbone. Sugar puckering is reproduced by the pm3 method for the four bases in the dT–pdA duplex. pm3 underestimates the attractive stacking interactions of base pairs in a B-DNA helical conformation. The performance of the pm3 method implemented in SPARTAN is contrasted with that implemented in MOPAC. At present, accurate ab initio calculations are too timeconsuming to be of practical use, and molecular mechanics methods cannot be used to determine quantum mechanical properties such as reaction-path calculations, transition-state structures, and activation energies. The pm3 method should be used with extreme caution for examination of small DNA systems. Future parameterizations of semiempirical methods should incorporate base stacking interactions into the parameterization data set to enhance the ability of these methods.

GROUPS THAT INVOLVE FINITELY MANY PRIMES AND HAVE ALL SUBGROUPS SUBNORMAL II

It is shown that if G is a hypercentral group with all subgroups subnormal, and if the torsion subgroup of G is a pi-group for some finite set pi of primes, then G is nilpotent. In the case where G is not hypercentral there is a section of G that is much like one of the well-known Heineken-Mohamed groups. It is also shown that if G is a residually nilpotent group with all subgroups subnormal whose torsion subgroup satisfies the above condition then G is nilpotent.

Static and Dynamic Error Correction of a Computer-Aided Mechanical Navigation Linkage for Arthroscopic Hip Surgery

While beneficially decreasing the necessary incision size, arthroscopic hip surgery increases the surgical complexity due to loss of joint visibility. To ease such difficulty, a computer-aided mechanical navigation system was developed to present the location of the surgical tool relative to the patient¿s hip joint. A preliminary study reduced the position error of the tracking linkage with limited static testing trials. In this study, a correction method, including a rotational correction factor and a length correction function, was developed through more in-depth static testing. The developed correction method was then applied to additional static and dynamic testing trials to evaluate its effectiveness. For static testing, the position error decreased from an average of 0.384 inches to 0.153 inches, with an error reduction of 60.5%. Three parameters utilized to quantify error reduction of dynamic testing did not show consistent results. The vertex coordinates achieved 29.4% of error reduction, yet with large variation in the upper vertex. The triangular area error was reduced by 5.37%, however inconsistent among all five dynamic trials. Error of vertex angles increased, indicating a shape torsion using the developed correction method. While the established correction method effectively and consistently reduced position error in static testing, it did not present consistent results in dynamic trials. More dynamic paramters should be explored to quantify error reduction of dynamic testing, and more in-depth dynamic testing methodology should be conducted to further improve the accuracy of the computer-aided nagivation system.