The number of spanning trees in a class of directed circulant graphs with generators depending linearly on the number of vertices \(\beta n\), and in the nth and \((n-1)\)th power graphs of the \(\beta n\)-cycle are evaluated as a product of \(\lceil \beta /2\rceil -1\) terms. 相似文献
We previously analyzed the Fab-1:VEGF (vascular endothelial growth factor) system described in this work, with both native top-down mass spectrometry and bottom-up mass spectrometry (carboxyl-group or GEE footprinting) techniques. This work continues bottom-up mass spectrometry analysis using a fast photochemical oxidation of proteins (FPOP) platform to map the solution binding interface of VEGF and a fragment antigen binding region of an antibody (Fab-1). In this study, we use FPOP to compare the changes in solvent accessibility by quantitating the extent of oxidative modification in the unbound versus bound states. Determining the changes in solvent accessibility enables the inference of the protein binding sites (epitope and paratopes) and a comparison to the previously published Fab-1:VEGF crystal structure, adding to the top-down and bottom-up data. Using this method, we investigated peptide-level and residue-level changes in solvent accessibility between the unbound proteins and bound complex. Mapping these data onto the Fab-1:VEGF crystal structure enabled successful characterization of both the binding region and regions of remote conformation changes. These data, coupled with our previous higher order structure (HOS) studies, demonstrate the value of a comprehensive toolbox of methods for identifying the putative epitopes and paratopes for biotherapeutic antibodies.
In this work we undertake a pioneer information‐theoretical analysis of 18 selected amino acids extracted from a natural protein, bacteriorhodopsin (1C3W). The conformational structures of each amino acid are analyzed by use of various quantum chemistry methodologies at high levels of theory: HF, M062X and CISD(Full). The Shannon entropy, Fisher information and disequilibrium are determined to grasp the spatial spreading features of delocalizability, order and uniformity of the optimized structures. These three entropic measures uniquely characterize all amino acids through a predominant information‐theoretic quality scheme (PIQS), which gathers all chemical families by means of three major spreading features: delocalization, narrowness and uniformity. This scheme recognizes four major chemical families: aliphatic (delocalized), aromatic (delocalized), electro‐attractive (narrowed) and tiny (uniform). All chemical families recognized by the existing energy‐based classifications are embraced by this entropic scheme. Finally, novel chemical patterns are shown in the information planes associated with the PIQS entropic measures. 相似文献
This study evaluates a combined protocol consisting of breath hold immediate post gadolinium 3-D gradient echo MR angiography and blood pool phase gadolinium-enhanced breath hold 2-D fat-suppressed spoiled gradient echo (SGE) sequences in the examination of diseases of the abdominal aorta and iliac vessels. Thirty-two patients with suspected disease of the abdominal aorta, major aortic branches, or iliac vessels underwent MR angiographic study from January 1996 to January 1997. Examinations were performed on a 1.5 T MR imager using 2-D axial SGE, coronal 3-D fast imaging in steady state precession (3-D FISP) following bolus administration of 40 mL of gadolinium, and axial and coronal blood pool phase gadolinium-enhanced fat-suppressed SGE. Post-processed data, including 3-D reconstructions using maximum intensity projection (MIP), targeted MIP, and multiplanar reconstruction (MPR) were evaluated. MR findings in all patients were correlated as follows: surgery (13 patients), angiography (11 patients), contrast enhanced CT (3 patients), non-contrast enhanced CT (1 patient), color doppler US (2 patients), and previous MR study (2 patients). MR findings correlated closely with findings at surgery or other imaging studies in 31 of 32 patients. One patient had renal artery occlusion that was misinterpreted as mild stenosis. The following vascular diseases were present: aneurysm disease [10 patients: aortic aneurysm (8 patients), inflammatory aneurysm (2 patients)], thoracoabdominal aortic dissection (2 patients), arteriovenous fistula (1 patient), stenoses and/or occlusion of the abdominal aorta, major aortic branches and iliac vessels [12 patients: stenoses and/or occlusion of the abdominal aorta with stenoses of the iliac vessels (9 patients), renal artery stenosis (2 patients), occlusion of the abdominal aorta (1 patient)], and occluded artery to pancreatic transplant artery (1 patient). Five patients had normal studies. The 3-D FISP technique accurately defined the luminal contours of vessels, allowing precise depiction of vessel stenosis (i.e., renal artery stenosis or common iliac artery stenosis) and clear demonstration of relationship of aortic branch vessels (i.e., renal arteries) to underlying aortic pathology (i.e., aortic aneurysm or dissection). Blood pool phase gadolinium-enhanced fat-suppressed SGE images were useful in the evaluation of the external surface of vessel walls, and providing accurate measurement of aneurysm diameter and other associated vascular entities (i.e., inflammatory aneurysm, left-sided IVC). Targeted MIP or MPR reconstruction were important for assessing stenoses of medium sized vessels such as renal arteries and branches of the iliac arteries, and for identifying accessory arteries. The combination of immediate post gadolinium 3-D FISP and blood pool phase gadolinium-enhanced fat-suppressed SGE is useful in the evaluation of the abdominal aorta, major aortic branches and iliac vessels. Immediate post gadolinium 3-D FISP images provides diagnostically useful information regarding vessel luminal contour, while blood pool phase gadolinium-enhanced fat-suppressed SGE provides ancillary information on the vessel wall and surrounding tissue. 相似文献
The structural and thermodynamic properties of TiAl intermetallics under high pressure have been investigated by ab initio plane-wave pseudopotential density functional theory method.It is found that the ratio of lattice parameter c to a keeps almost constant with a value of 1.02 under the pressure from 0 to 20 GPa,which agrees well with the experimental results.With the pressure increasing from 20 to 45 GPa the values of c/a decrease almost linearly from 1.02 to 0.99.These calculated results indicate under low pressure the variation rate for a-axis is almost the same to that for c-axis,but under higher pressure the variation for a-axis is smaller than along c-axis.Through the quasi-harmonic Debye model,the equation of state(EOS) of TiAl intermetallics,as well as the thermal expansion and heat capacity at various pressures and temperatures are also studied. 相似文献
Theoretical calculations (B3LYP/6–311+ +G**) were performed on a series of formally hypervalent compounds showing linear
three-center geometries. The bonding nature was analyzed by the electron density, ρ(r), and electron-localization function
(ELF) topologies, including calculations of the AIM charges and NMR chemical shifts (GIAO method). In addition, a quantitative
analysis was also performed of the localization and delocalization indexes, obtained from the electron-pair density in conjunction
with the definition of an atom in a molecule. Furthermore, the populations and fluctuations in the ELF basins were also evaluated.
The compounds studied presented linear (1–5), T-shaped (6–9), and bipyramidal structures (10–15). Our results support the 3c-4e model for the linear (1–5) structures, but reveal for the T-shaped (6–9) structures only a small contribution from this model. In addition, there is no evidence to support the 3c-4e bond scheme
for the bipyramidal compounds (10–15).
Received: 1 June 2000 / Accepted: 4 October 2000 / Published online: 19 January 2001 相似文献