Primitive translations

Palchetti I, Mascini M (2005) Electrochemical Adsorption Technique for Immobilization of Single-Stranded Oligonucleotides onto Carbon Screen-Printed Electrodes. 261 27-43 Pascal R, Boiteau L, Commeyras A (2005) From the Prebiotic Synthesis of a-Amino Acids Towards a Primitive Translation Apparatus for the Synthesis of Peptides. 259 69-122 Paulo A, see Santos I (2005) 252 45-84 Perez EM, see Leigh DA (2006) 265 185-208 Perret F, see Coleman AW (2007) 277 31-88 Perron H, see Coleman AW (2007) 277 31-88 Pianowski Z, see Winssinger N (2007) 278 311-342 Piestert F, see Gansauer A (2007) 279 25-52... 

From the above properties it is evident that the set of operations t forms a group, J the space group of the crystal. If the translation operations are the primitive translations is r , ... 

Pascal R, Boiteau L, Commeyras A (2005) From the Prebiotic Synthesis of a-Amino Acids Towards a Primitive Translation Apparatus for the Synthesis of Peptides. 259 69-122 Paulo A, see Santos I (2005) 252 45-84... 

Primitive translation system develops, with RNA genome and RNA-protein catalysts... 

Let the primitive translations in the real lattice be the vectors a, b, c, then these quantities multiplied by the integers u, v, w, respectively define the lattice points. Thus... 

In a similar manner let the primitive translations in the reciprocal lattice be the vectors a, b c corresponding to the integers h, k, /. (The asterisk here denotes the reciprocal lattice, not a complex conjugate.) The reciprocal lattice vectors are defined implicitly by the equations... 

From the Prebiotic Synthesis of a-Amino Acids Towards a Primitive Translation Apparatus for the Synthesis of Peptides... 

Theorem — Let G be a bipartite regular polymer graph G with cyclic boundary conditions and with a Kekule structure K, which has edge set (K). Then the difference 8(G,e,K) between the orders of e n (K) and of es+n (K) for translationally equivalent boundary sets e varies with a period of no more than 2. The period can only be 2 if the primitive translation interchanges starred unstarred sites. 

The strips may be divided into unit cells or eventually reduced unit cells (see Fig. 1), when the space group of the strip contains operations involving glide-reflections or screw-rotations, i.e. a combination of an improper reflection or two-fold rotation followed by a non-primitive translation of half a unit cell, which by themselves do not leave the lattice invariant. Each cell will contain w sites, w x L = 2N. 

Along with the primitive translations, and glide-reflections when appropriate, there axe other symmetry operations belonging to the space group. In bipartite systems, it is relevant to classify any symmetry operation according to whether it leaves each sublattice invariant or transforms one into each other (see, for instance, Fig. 2). 

Pascal R, Boiteau L, Commeyras A. From the prebiotic synthesis of a-amino acids towards a primitive translation apparatus for the synthesis of peptides. Top Curr Chem 2005 259 69-122. 

A more accurate replication required protein enzymes, but the synthesis of these enzymes required a primitive translation apparatus, and therefore the presence of genes for such an apparatus. The smallest genome that is capable of coding for a replicase and a rudimentary translation apparatus is not known, but it has been estimated that a minimum of ten genes is necessary in order to keep translation errors within tolerable limits. The appearance of a primitive genome presents, however, two contrasting problems. 

One of the main bacterial features is the fact that DNA transcription is immediately followed by translation, to the extent that in most cases protein synthesis starts on primary transcripts that are still attached to DNA. The result is that there is neither the time nor the space for a modification of the transcripts. In the ribotype world, on the other hand, the first nucleic acids were mostly random molecules, and the first systems were necessarily full of statistical RNAs. It is likely therefore that some kind of screening had to be made before protein synthesis, which means that primitive translation was taking place some time after primitive transcription. A system that contains both useful and useless RNAs is more primitive than a system in which all RNAs are useful, and so it is likely that in the common ancestor transcription was separated from translation. 

Zones bounded by planes defined by equation 38 are consistent with the reduced-vector zones. These reciprocal-lattice planes are simply the planes bisecting the vectors K and normal to them. It is noteworthy that lattices with the same type of translational symmetry have equivalent zone patterns since zone structure is determined by the K vectors, and these are determined by the primitive translation vectors. 

A crystal is a physical object - it can be touched. However, an abstract construction in Euclidean space may be envisioned, known as a direct space lattice (also referred to as the real space lattice, space lattice, or just lattice for short), which is comprised of equidistant lattice points representing the geometric centers of the structural motifs. Any two of these lattice points are connected by a primitive translation vector, r, given by ... 

Fixed-Point-Free Motions. These include translations, screw rotations, and glide reflections. Because the primitive translation vector, Eq. 1.2, joins any two lattice points, an equivalent statement is that Eq. 1.2 represents the operation of translational symmetry bringing one lattice point into coincidence with another. However, we must choose the basis vectors (a, b, c) so as to include all lattice points, thus defining a... 

It has just been stated that a band stracture diagram is a plot of the energies of the various bands in a periodic solid versus the value of the reciprocal-space wave vector k. It is now necessary to discuss the concept of the reciprocal-space lattice and its relation to the real-space lattice. The crystal structure of a solid is ordinarily presented in terms of the real-space lattice comprised of lattice points, which have an associated atom or group of atoms whose positions can be referred to them. Two real-space lattice points are connected by a primitive translation vector, R ... 

TABLE 4.1. Primitive Translation Vectors of the Real-Space Cubic Lattices R = ua- + v32 + was... 

Taking the primitive translation vectors for one of the real-space cubic lattices from Table 4.1, Eqs. 4.25-4.27 can be used to obtain the primitive translation vectors for the corresponding reciprocal lattice, which are given in Table 4.2. By comparing Tables 4.1 and 4.2, it is seen that the primitive vectors of the reciprocal lattice for the real-space FCC lattice, for example, are the primitive vectors for a BCC lattice. In other words, the ECC real-space lattice has a BCC reciprocal lattice. 

What are the primitive translation vectors of the reciprocal lattice ... 

Like the diamond stracmre discussed earlier, the honeycomb stracture is not itself a Bravais lattice. If the lattice is translated by one nearest-neighbor distance, the lattice does not go into itself. There are two nonequivalent, or distinct types of sites per unit cell, atoms a and b, separated by a distance Uq, as shown later in Figure 4.6. However, a Bravais lattice can be created by taking this pair of distinct atoms to serve as the basis. Doing so, shows that the vectors of the two-dimensional hexagonal lattice, a and U2, are primitive translation vectors. A given site on one sublattice with coordinates (0, 0), has three nearest neighbors on the other sublattice. They are located at (0, U2), (fli, 0), and (- , 0). 

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