Implicit sequences

Rauch, S.L., Savage, C.R., Alpert, N.M., Dougherty, D., Kendrick, A., Curran, T., Brown, H.D., Manzo, P., Fischman, A.J., and Jenike, M.A. (1997) Probing striatal function in obsessive-compulsive disorder a PET study of implicit sequence learning. J Neuropsychiatry Clin Neurosci 9 568-573. 

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. 

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. 

Figure 5.3. Testing a three-dimensional viewer for sequence numbering artifacts with the structure 3TS1 (Brick et al., 1989). WebMol, a Java applet, correctly indicates both the explicit and implicit sequences of the structure. Note the off-by-two difference in the numbering in the two columns of numbers in the inset window on the lower right. The actual sequence embedded in the PDB file is 419 residues long, but the COOH-terminal portion of the protein is lacking coordinates it also has two missing residues. (See color plate.)...

We can further subdivide implicit scheme searches into two categories. If the eocact product of one reaction is used as the reactant in another reaction, then the connection between the two reactions is by exact-structure, and is referred to here as a first-order imphcit sequence. If the connection between the two reactions is by inexact structure match (such as two highly similar molecules), then we refer to it as a second-order implicit sequence. This latter type of search has much in common with synthesis planning programs it has the most to offer, but poses the greatest technical challenge. 

Any program that can be used to find implicit schemes will also find explicit schemes. The added value of a search over implicit schemes will be based on the number of additional answers an implicit search provides, which in general is determined by the number of independent reactions sharing common molecules. The diversity of the chemistry, the unusualness of the molecules, and the ratio of reactions to molecules in the database will all have an effect on the volume of results of implicit sequence searches. 

Often precedence for a proposed reaction scheme cannot be found using a single molecidar system. Valuable answers to questions can be missed if part of a proposed scheme operates on a molecular system only slightly different than other parts often the difference between the two molecular systems is inconsequential to the success of the proposed scheme. Schemes whose connections between reactions are based on non-identical structures can be referred to as Second-Order Implicit sequences. The connections between reaction participants can be based on a variety of relationships ... 

One can think of approaches to second-order implicit schemes in terms of how this ratio can be increased in a database. One approach is to reduce artificially the number of molecules in the database another is to increase the number of reactions, while holding the number of molecules constant. There is an important difference between approaches to second-order implicit sequences, and the t3q>es of schemes described previously. ExpUcit and first-order implicit schemes consist entirely of recorded fact, and are guaranteed to work in the laboratory. In order to rebalance the equation to return more answers to scheme queries, some abstract or empirical chemical knowledge must be used the process reliability is therefore not guaranteed, and the quality of results obtained will be based largely on the viabihty and generality of the rules by which the balance of the equation is modified. 

However, by constructing a nested sequence of successively larger discrete spaces and approximations therein we hope to end up with some approximation of a unique invariant measure, which is then implicitly defined via the constructed sequence of subspaces. An expression of this mathematical consideration is the multilevel structure of the suggested algorithm - details see below (Section 3.2). In physical terms, we hope that the perturbations introduced by discretization induce a unique and smooth invariant measure but are so weak that they do not destroy the essential physical structure of the problem. 

Implicit in the presumption of folding pathways is the existence of intermediate, partially folded conformational states. The notion of intermediate states on the pathway to a tertiary structure raises the possibility that segments of a protein might independently adopt local and well-defined secondary structures (a-helices and /3-sheets). The tendency of a peptide segment to prefer a particular secondary structure depends in turn on its amino acid composition and sequence. 

Despite being notoriously difficult to analyze formally, the behavior of general CA rules is nonetheless often amenable to an almost complete mathematical characterization. In this section we look at a simple method that exploits the properties of certain implicit deterministic structures of elementary one-dimensional rules to help determine the existence of periodic temporal sequences, rule inverses and homogeneous states. Additional details appear in [jen86a] and[jen86b]. 

In traditional treatments of copolymerizaiion kinetics, the values of the ratios sA and % are implicitly set equal to unity (Section 7.3.1.2.2). Since they contain no terms from cross propagation, these parameters have no direct influence on either the overall copolymer composition or the monomer sequence distribution they only influence the rate of polymerization. 

Surface carbon hydrogenation occurs through a sequence of hydrogenation steps in which CH, ads species are formed with increasing hydrogenation, rn, the rate of C ds hydrogenation, depends implicitly on hydrogen pressure. 

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. 

Implicit in the use of the term sequence of molecular events is the idea that the chemical transformation that one observes in the laboratory is not the result of a single molecular process but is the end result of a number of such processes. If one considers reactions such as... 

Implicit in the functioning of the Watson-Crick DNA model is the idea that the strands of a DNA molecule must separate and new daughter strands must be synthesized in response to the sequence of bases in the mother strand. This is called semiconservative replication. Still, conservative replication, in which both strands of a daughter molecule are newly synthesized, could not be ruled out by consideration of the structure of DNA alone. 

The LP solutions in the nodes control the sequence in which the nodes are visited and provide conservative lower bounds (in case of minimization problems) with respect to the objective on the subsequent subproblems. If this lower bound is higher than the objective of the best feasible solution found so far, the subsequent nodes can be excluded from the search without excluding the optimal solution. Each feasible solution corresponds to a leaf node and provides a conservative upper bound on the optimal solution. This combination of branching and bounding or cutting steps leads to the implicit enumeration of all integer solutions without having to visit all leaf nodes. 

In the bioinformatics realm, SRS (Sequence Retrieval System) [2] is a popular system, which uses a centralized collection of data resources primarily in flat text file form and, more recently, handles XML (Extensible Markup Language) files as well. Data resources are treated in a federated manner since each is maintained in its original form. However, SRS contains a large number of cross-references between corresponding fields in various data sources, so that keyword searches can be done across them. SRS thus performs more structured searches across the information than what a simple text search provides (such as web indexes perform, for example). Even though the data model implicit in the cross-reference tables is not very deep, SRS provides a useful way for users to browse and do simple queries across a large number of data sources as well as to integrate results from some computational methods. 

The implicit penultimate model was proposed for copolymerizations where the terminal model described the copolymer composition and monomer sequence distribution, but not the propagation rate and rate constant. There is no penultimate effect on the monomer reactivity ratios, which corresponds to... 

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