Loop formation

Stitch formation with slide and spring needles is similar, the main difference being that the hook of the compound needle has to be closed with a separate slide. The hook of the spring needle is closed by pressing the spring of the hook into the slot in the shaft. 

For the production of plain or purl fabrics, a second needle system is required. Loop formation for one-by-one rib and interlock knittings is shown in Fig. 5.5. 

To raise the needles, special parts in the cam box are required. The needle feet are guided in channels inside the cam parts. There are three different cam part types used for forming loops, as shown in Fig. 5.6. 

In order to produce a simple mesh, cams are required that can raise the needle to Its highest point where the actual mesh Is formed (knitting). Other cam parts can raise the needle only to a middle position (tuck position), which results In a loop. Other cams do not raise the needle at all and create float stitches. 

Meshes are built across one or several courses Several meshes are close together Tuck position of the needle 

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J. Campos-Delgado, Y.A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R.D. Shull, M.S. Dresselhaus, M. Terrones, Thermal stability studies of CVD-grown graphene nanoribbons Defect annealing and loop formation, Chemical Physics Letters, vol. 469, pp. 177-182, 2009. 

Figure 20. Steps involved in loop formation, (a) Free evolution of the tube in depletive environment (b) formation of an unstable loop at around 3.4 lp (c) gliding of the loop governed by the positions of the two contact points along the fiber and the entry-exit angle (d) trapping of the loop by local defects. The translucent green surface represents the excluded volume for the fluid of hard spheres in (b,c,d) one sees that some of the excluded volume is reduced from the overlap resulting from formation of the loop. See color insert.

S. Jun, J. Bechhoefer, andB.-Y. Ha, Diffusion-limited loop formation of semiflexible polymers Kramers theory and the intertwined time scales of chain relaxation and closing. Europhys. Lett. 64, 420-426 (2003). 

In the present paper, theoretical arguments and modulus measurements are used to deduce the significant gel structures which lead to inelastic loop formation and to quantify the network defects and reductions in modulus which may be expected, even in the limit of no pre-gel intramolecular reaction. In this limit all the existing theories and computer simulations of polymerisations including intramolecular reactlon(8,10,ll) predict that perfect networks are formed. 

Table I. Values of parameters characterising pre-gel intramolecular reaction (v,b,(f-2)/(vb ) ) (5-7,12) and the extents of post-gel intramolecular reaction which, in the limit of ideal gelling systems, lead to inelastic loop formation at complete reaction (p g). The values of pj g define the indicated values of Mg/M° and the reductions in shear moduli of the dry networks relative to those of the perfect networks (G/G° = Mc/Mc). The values of Pr g in the limit of reactants of infinite molar mass (v = < ) are denoted p°>°° in the text...

The positive intercepts in Figure 7 show that post-gel(inelastic) loop formation is influenced by the same factors as pre-gel intramolecular reaction but is not determined solely by them. The important conclusion is that imperfections still occur in the limit of infinite reactant molar masses or very stiff chains (vb - ). They are a demonstration of a law-of-mass-action effect. Because they are intercepts in the limit vb - >, spatial correlations between reacting groups are absent and random reaction occurs. Intramolecular reaction occurs post-gel simply because of the unlimited number of groups per molecule in the gel fraction. The present values of p , (0.06 for f=3 and 0.03 for f=4 are derived from modulus measure- ments, assuming two junction points per lost per inelastic loop in f=3 networks and one junction point lost per loop in f=4 networks. 

Significant Structures for Inelastic Loop Formation under Conditions of Random Reaction... 

It is impossible to specify in detail all the isomeric structures which occur as a network is forming. However, with regard to one-membered loop formation, two extreme types may be delineated, namely, linear and symmetric isomers. They are illustrated in Figure 9 for an RA polymerisation. Linear isomers are able to form the smallest number of one-membered loops and symmetric isomers the largest number. In an RAf polymerisation, for linear isomers of n units, the total number of pairs of unreacted ends for intramolecular reaction is... 

The case of RAf polymerisations has been evaluated and the experimentally deduced values of Pg g interpreted in terms of one-membered loop formation within structures of defined size. The knowledge of such structures is important for theories of non-linear polymerisations and network formation. Theories have to simplify in some way the infinite numbers of structures which actually occur and it is important that those significant for intramolecular reaction are retained. In this context, it should be noted that present theories assume that ideal gelling systems lead to perfect networks. The approximation needs to be removed as it is inconsistent with the structure of the growing gel, a molecule with unlimited pairs of groups for intramolecular reaction. 

On the other hand, it might be conjectured that normally paired bases at the ends of DNA molecules might transiently unpair, and then form intermolecularly base-paired complexes. Since the DNA studied is short, melting in the middle of the duplex (loop formation) is extremely unlikely, and the single sequence approximation, with melting from the ends only, is well satisfied. 

This concept of reversible chemical crosslinking of the chains to drastically decrease the enthalpic penalty of the folding process and to exploit the highly favored disulfide loop formation in the A-chain with m = 4, has been further developed into artificial peptide linker chains that can be excised selectively by enzymatic processing, to allow for bioexpression of the artificial proinsulins on an industrial scale. 95,96 However, to apply this approach rationally to other double-stranded cystine peptides, knowledge about their three-dimensional structure is essential. 

Fig. 1.19. Tetramerization of the Lac repressor and loop formation of the DNA. The Lac repressor from E. coli binds as a dimer to the two-fold symmetric operator seqnence, whereby each of the monomers contacts a half-site of a recognition sequence. The Lac operon of E. coli possesses three operator sequences Of, 02 and 03, aU three of which are required for complete repression. Of and 03 are separated by 93 bp, and only these two sequences are displayed in the figure above. Between Of and 03 is a binding site for the CAP protein and the contact surface for the RNA polymerase. The Lac repressor acts as a tetramer. It is therefore assumed that two dimers of the repressor associate to form the active tetramer, whereby one of the two dimers is bound to 03, the other dimer binds to Of. The intervening DNA forms a so-caUed repression loop. After Lewis et al., 1996.

This type of promoter displays markedly different characteristics compared to the o -dependent promoter. The o -contammg holoenzyme binds tightly to the promoter in the absence of transcriptional activators. In this closed state, however, it is not capable of initiating transcription. The transcriptional activators are required in this case to activate the promoter-bound holoenzyme for initiation, i.e. to transform it into the open complex (see Fig. 1.29). Activation is mediated via protein-protein interactions between the transcriptional activator and the RNA polymerase holoenzyme, and is accompanied by ATP hydrolysis. The binding site for the transcriptional activator is found at a distance of ca.llO bp upstream form the start site and can be shifted further upstream without loss of stimulatory effect. Direct interaction of the holoenzyme with the bound transcriptional activator is possible due to loop formation of the intervening DNA. The strict dependency on transcriptional activators for transcription initiation indicates that the DNA-bound holoenzyme alone is not capable of isomerizing to the transcription-competent open complex. The transition to the open complex requires interactions with the transcriptional activator, an event which occurs with ATP hydrolysis. 

Fig. 1.29. Mechanism of promoter activation of (/ -dependent genes in procaryotes. The formation of an open, initiation-competent transcription complex for (/ -dependent genes requires the assistance of transcription activators, which bind to their cognate UAS element. Upon loop formation of the intervening DNA sequences, the transcription activator interacts with the (/ -con-taing RNA polymerase bound to the promoter. The activation is accompanied by ATP hydrolysis and leads to the formation of an open complex.

The point at which the homoclinic orbit is formed must be calculated numerically, but once it has been located we can show that the limit cycle is still unstable as it approaches the loop formation. We do this by evaluating the trace of the Jacobian matrix for the saddle point solution a2, P2 corresponding to Tres if tr(J) is positive, the limit cycle is unstable (as we always find for this special case of the present model) if tr( J) is negative for the saddle... 

N 124 "Loop Formation in Polynucleotide Chains. I. Theory of Hairpin Loop Closure"... 

A theoretical model to determine the probability of loop formation, based on an elaborated form of the Jacobson-Stockmayer theory of cyclization equilibria, is developed and used on RNA chains of homogeneous puckering and lengths up to 2 residues. 

N 130 "Loop Formation in Polynucleotide Chains. II. Flexibility of the Anticodon Loop of fRNAphe "... 

Branching and crosslinking processes can be treated as a combinatorial problem which is not too complicated when the functionalities are equally reactive and unreacted functionalities are considered as the only kind of defects. If loop formation (intra-molecular cyclization) is involved, the complexity increases considerably. The same holds if the monomers contain groups of unequal reactivity or if the reactivity is influenced by substitution effects. 

In the foregoing consideration the effect of intramolecular cross-linking on network formation and the gel point was not taken into account. In reality intermolecular crosslinking is always accompanied by closed loop formation. Every new bond between segments of the same (branched) polymer chain is an intramolecular crosslink if it does not increase its molecular weight. In a network a crosslink is intermolecular... 

In this case the concentration of chemically introduced crosslinks, vf, was accurately known. Assuming that there are no entanglements and no wasted crosslinks through loop formation the concentration of chemically formed network chains equals the effective number of chains, v. Proceeding in this way Van de Kraats found for a series of three gels that B = 0.5 0.1. Of course, this result should be viewed with caution because the assumption vf — r is open to some doubt. An estimate of the error on the basis of the considerations of Chapter II, Section 2.2 is not reasonably feasible. The data, of course, also yield A /B. 

Reactions catalyzed by purified recA protein in vitro. RecA catalyzes a number of different reactions between DNA strands, all of them involving the unwinding and winding of base-paired structures, (a) D-loop formation by interaction between supercoiled circular duplex DNA and single-stranded DNA. (b) Strand exchange between a gapped circular duplex structure and a linear duplex structure, (c) Complex formation between two helices, one of which is gapped. 

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