Truncated chains

As mentioned throughout the previous sections, it is important to emphasize the role of electroneutrality in the formation of truncated chains, products that obviously hold potential for a further increase in the nuclearity of the cyanide-bridged core. An excellent illustration of this point is the structure of [Ho (dmQ3(H20)3]2[Ni°(CN)4]3] (189). Earher, we described a large family of complexes composed of rare earth Ln(III) and [M (CN)6] ions (M = Cr, Fe, Co) (Table I). The combination of these ions in a 1 1 ratio results in neutral dimers that readily crystallize from solutions in DMF or DMSO. In contrast, the cluster that... 

It is important to note at this stage that the use of a truncation chain length in the simulations impedes the use of equation 3.34. This equation requires integration over the complete MWD, which is not available from the simulation output. To deal with this problem, it is necessary to use additional information that is available from the simulations. Beside the number of radicals at time / = 0, also the number of radicals that are still present when the simulation is stopped must be known. As termination is assumed to occur exclusively by combination, this number of residual radicals actually represents twice the number of polymer chains that are missing in the number distribution because of the limited time-span over which the simulations were performed. Hence, with knowledge about the concentration of residual radicals, denoted as [7 ], the integral in equation 3.34 can be replaced by ... 

Residual Bath Subspace Stars, Chains, and Truncated Chains... 

Fig. 15.1 Schematic illustration of the coupling patterns within the residual-mode subspace, as described in Sect. 15.2.3. The number of effective modes is N ff = 3 in the present example. L Star type pattern, with a diagonal form of the djj matrix in the residual Ng —iVeff)-dimensional subspace middle chain type configuration with a band-diagonal form right truncated chain pattern which re-introduces the star pattern at a higher order of the chain...

Truncated chain-type configuration of the residual bath (see Fig. 15.1, right panel). This variant again employs the band-diagonal construction of the chain model, but is terminated at a given order M by a star construction as described above, now taken to represent a Markovian closure acting on the end of the chain [32]. This model mimicks the Markovian closure which naturally terminates the chain as shown in the next section. 

Based upon the effective-mode construction, a systematic approximation procedure for the environment can be formulated in terms of a series of coarse-grained spectral densities [32,33]. These spectral densities are generated from successive orders of a truncated chain model with Markovian closure. Analytical expressions can be given in terms of Mori type continued fractions. Assuming that an - a priori arbitrarily complicated - reference spectral density can be obtained independently, e.g., from experiments or classical simulations, one can thus (1) extract those features of the spectral density that determine the interaction with the subsystem... 

This series expansion is truncated at a specified order and is probably most easily implemei ted within a predictor-corrector type of algorithm, where the higher-order terms are ahead computed. This method has been applied to relatively simple systems such as molecuh fluids [Streett et al. 1978] and alkane chain liquids [Swindoll and Haile 1984]. 

Truncated Forms. Tmncated forms of hGH have been produced, either through the actions of enzymes or by genetic methods. 2-CAP, generated by the controlled actions of the trypsin, has the first eight residues at the N-terminus of hGH removed. Other tmncated versions of hGH have been produced by modification of the gene before expression in a suitable host. The first 13 residues have been removed to yield a derivative having distinctive biological properties (30). In this latter case the polypeptide chain is not cleaved. 

The use of QM-MD as opposed to QM-MM minimization techniques is computationally intensive and thus precluded the use of an ab initio or density functional method for the quantum region. This study was performed with an AMi Hamiltonian, and the first step of the dephosphorylation reaction was studied (see Fig. 4). Because of the important role that phosphorus has in biological systems [62], phosphatase reactions have been studied extensively [63]. From experimental data it is believed that Cys-i2 and Asp-i29 residues are involved in the first step of the dephosphorylation reaction of BPTP [64,65]. Alaliambra et al. [30] included the side chains of the phosphorylated tyrosine, Cys-i2, and Asp-i 29 in the quantum region, with link atoms used at the quantum/classical boundaries. In this study the protein was not truncated and was surrounded with a 24 A radius sphere of water molecules. Stochastic boundary methods were applied [66]. 

These treatments of periodic parts of the dipole moment operator are supported by several studies which show that, for large oligomeric chains, the perturbed electronic density exhibits a periodic potential in the middle of the chain whereas the chain end effects are related to the charge transfer through the chain [20-21]. Obviously, approaches based on truncated dipole moment operators still need to demonstrate that the global polarization effects are accounted for. In other words, one has to ensure that the polymeric value corresponds to the asymptotic limit of the oligomeric results obtained with the full operator. 

The main apohpoprotein of LDL (P-lipopro-tein) is apohpoprotein B (B-lOO) and is found also in VLDL. Chylomicrons contain a truncated form of apo B (B-48) that is synthesized in the intestine, while B-lOO is synthesized in the hver. Apo B-lOO is one of the longest single polypeptide chains known, having 4536 amino acids and a molecular mass of 550,000 Da. Apo B-48 (48% of B-lOO) is formed from the same mRNA as apo B-lOO after the introduction of a stop signal by an RNA editing enzyme. Apo C-1, C-11, and C-111 are smaller polypeptides (molecular mass 7000— 9000 Da) freely transferable between several different hpoproteins. Apo E is foimd in VLDL, HDL, chylomicrons, and chylomicron remnants it accounts for 5— 10% of total VLDL apohpoproteins in normal subjects. 

Isoelectric focusing of transferrin is a useful biochemical test for assisting in the diagnosis of these conditions truncation of the oligosaccharide chains of this protein alters its isolectric focusing pattern... 

Metabolic oxidation of the sulfonamide propyl chain was found to be problematic. Truncation to the ethyl analog 22 resulted in good potency... 

This approximation amounts to truncating the functional expansion of the excess free energy at second order in the density profile. This approach is accurate for Lennard-Jones fluids under some conditions, but has fallen out of favor because it is not capable of describing wetting transitions and coexisting liquid-vapor phases [105-107]. Incidentally, this approximation is identical to the hypemetted chain closure to the wall-OZ equation [103]. 

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