Explicit sequence

PDB file-encoded sequences are notoriously troublesome for programmers to work with. Because completeness of a structure is not always guaranteed, PDB records contain two copies of the sequence information an explicit sequence and an implicit sequence. Both are required to reconstruct the chemical graph of a biopolymer. 

Explicit sequences in a PDB hie are provided in lines starting with the keyword SEQRES. Unlike other sequence databases, PDB records use the three-letter amino acid code, and nonstandard amino acids are found in many PDB record sequence entries with arbitrarily chosen three-letter names. Unfortunately, PDB records seem to lack sensible, consistent rules. In the past, some double-helical nucleic acid sequence entries in PDB were specihed in a 3 -to-5 order in an entry above the complementary strand, given in 5 -to-3 order. Although the sequences may be obvious to a user as a representation of a double helix, the 3 -to-5 explicit sequences are nonsense to a computer. Fortunately, the NDB project has hxed many of these types of problems, but the PDB data format is still open to ambiguity disasters from the standpoint of computer readability. As an aside, the most troubling glitch is the inability to encode element type separately from the atom name. Examples of where... 

Consider an example in which the sequence ELVISISALIVES is represented in the SEQRES entry of a hypothetical PDB file, but the coordinate information is missing all (x, y, z) locations for the subsequence ISA. Software that reads the implicit sequence will often report the PDB sequence incorrectly from the chemical graph as ELVISLIVES. A test structure to determine whether software looks only at the implicit sequence is 3TS1 (Brick et al., 1989) as shown in the Java three-dimensional structure viewer WebMol in Eigure 5.3. Here, both the implicit and explicit sequences in the PDB file to the last residue with coordinates are correctly displayed. 

One of the most important examples of this is the semi-classical approximation to quantum mechanics in 1959 Ford and Wheeler [65] described the explicit sequence of approximations by which the rigorous quantum cross section of (2.1)-(2.3) degenerates to the completely classical cross section,... 

We examined two methodologies for searching explicit sequences prior... 

There is now a simple explicit expression for the vapor rate in a single column in terms of the feed to the column. In order to use this expression to screen column sequences, the vapor rate in each column must be calculated according to Eq. (5.8), assuming a sharp separation in each column, and the individual vapor rates summed. 

Cases have been reported where the application of the penultimate model provides a significantly better fit to experimental composition or monomer sequence distribution data. In these copolymerizations raab "bab and/or C BA rBBA- These include many copolymerizations of AN, 4 26 B,"7 MAH28" 5 and VC.30 In these cases, there is no doubt that the penultimate model (or some scheme other than the terminal model) is required. These systems arc said to show an explicit penultimate effect. In binary copolynierizations where the explicit penultimate model applies there may be between zero and three azeotropic compositions depending on the values of the reactivity ratios.31... 

Although no matrix V occurs explicitly in this sequence of transformations, it can be verified that for a V formed from vx = el9 the matrices are such that... 

The theory was very similar to that described earlier, but was simplified in view of the complexity of the problem. A number of reaction intermediates were considered explicitly, and the corresponding signals were calculated by molecular dynamics simulation. Kinetic equations governing the reaction sequence were established and were solved numerically. The main simplification of the theory is that, when calculating A5[r, r], the lower limit of the Fourier integral was shifted from 0 to a small value q. The authors wrote [59]... 

The solution of Problem-1 requires extensive search over the set of potential sequences of operations. Prior work has tried either to identify all feasible operating sequences through explicit search techniques, or locate the optimum sequence (for single-objective problems) through the implicit enumeration of plans. The former have been used primarily to solve planning problems with Boolean or integer variables, whereas the latter have applied to problems with integer and continuous decisions. 

In order to represent and reason with temporal information, we need to represent time explicitly and concisely. The discrete-time character of computer-aided data acquisition and control dictates that time should be represented as a sequence of strictly increasing time points ... 

Very similar to the STN is the state sequence network (SSN) that was proposed by Majozi and Zhu (2001). The fundamental, and perhaps subtle, distinction between the SSN and the STN is that the tasks are not explicitly declared in the SSN, but indirectly inferred by the changes in states. A change from one state to another, which is simply represented by an arc, implies the existence of a task. Consequently, the mathematical formulation that is founded on this recipe representation involves only states and not tasks. The strength of the SSN lies in its ability to utilize information pertaining to tasks and even the capacity of the units in which the tasks are conducted by simply tracking the flow of states within the network. Since this representation and its concomitant mathematical formulation constitute the cornerstone of this textbook, it is presented in detail in the next chapter. 

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