Non-random sequence

The rheological behaviour of thermotropic polymers is complex and not yet well understood. It is undoubtedly complicated in some cases by smectic phase formation and by variation in crystallinity arising from differences in thermal history. Such variations in crystallinity may be associated either with the rates of the physical processes of formation or destruction of crystallites, or with chemical redistribution of repeating units to produce non-random sequences. Since both shear history and thermal history affect the measured values of viscosity, and frequently neither is adequately defined, comparison of results between workers and between polymers is at present hazardous. 

From the picture presented in Fig. 7, one can expect that the sequential hydrophobization of a polymer coil should lead to a copolymer with a non-random sequence distribution. This is indeed the case. As an example, let us consider the average number fractions of blocks consisting of l neighboring amphiphilic monomers, /a( ), occurring in a copolymer chain. Some results are shown in Fig. 8 on a semilogarithmic scale. 

Copolymers are synthesized using exactly the same type of chemistry as homopolymers, of course, but everything depends on the way you do it. Step-growth polymerizations of two different monpmers often give you truly random copolymers, because rearrangement reactions like transesterification can scramble any initial non-random sequence distribution imposed by the kinet-... 

One potential problem with conventional free-radical copolymerization is that the reactivity ratios of the two monomers tend to be different from one another [6]. On one hand this leads to non-random sequences of the monomers on a single chain (usually the product of the reactivity ratios is less than one so that there is a tendency to form alternating sequences) and, on the other, to substantial composition drift if the polymerization is carried out in bulk to high conversions. Random copolymers with a range of compositions as a result of composition drift may however be useful in practice, allowing a compositionally graded interface to be formed. 

We may be concerned with imusually large numbers of short runs, as well as unusually small numbers of long runs. If six plus and six minus signs occurred in the order + - + - + - + - + - + -we would strongly suspect a non-random sequence. Table A.10 shows that, with N = M= 6, a total of 11 or 12 runs indicates that the null hypothesis of random order should be rejected, and some periodicity in the data suspected. 

Systematic error is evident in the clear ellipticity of the distribution. The time ordered sequence shows a non-random "walk" between systematic error quadrants. An excursion from one systematic quadrant to another and a subsequent return is evident. The distribution is non-normal, with too few points in the central region. 

The standard error is about 27., which is certainly not larger than the error in the observed rate coefficients. Therefore, the fit is acceptable in spite of some non randomness in the sequence of residuals. This conclusion is supported by the acceptable value of D-statistics, athough with only 10 data points we cannot use this test rigorously. 

Fig. 3.9. Diagram showing the principle of the nick-translation sequencing procedure. For the purpose of illustration the single unique product generated from one nicked molecule is shown. With a heterogeneous set of nicked duplexes nick-translation will proceed from each gap until terminated by the incorporation of a dideoxynucleotide. Since the corresponding deoxynucleotide is also incorporated in competition with the dideoxynucleotide, the eifect of non-random cleavage with DNAase I is minimized.

As a full-scale family classification system, more than 1200 MOTIFIND neural networks were implemented, one for each ProSite protein group. The training set for the neural networks consisted of both positive (ProSite family members) and negative (randomly selected non-members) sequences at a ratio of 1 to 2. ProClass groups non-redundant SwissProt and PIR protein sequence entries into families as defined collectively by PIR superfamilies and ProSite patterns. By joining global and motif similarities in a single classification scheme, ProClass helps to reveal domain and family relationships, and classify multi-domained proteins. 

It is interesting to note that although apparently unaware of the development of molecular imprinting, Pande et al. [28] proposed the use of thermodynamic control for the preparation of synthetic polymer systems with a memory for a template structure. Monte Carlo computer simulations were performed to validate their hypothesis. From these calculations they identified the formation of non-random polymer sequences arising from an evolution-like preferred selection of various monomer components by similar species. These studies have since been expanded upon using statistical mechanics to examine the consequences for protein folding [29]. 

Figure 21. Mutant space high-value contour near local optimum. Diagram is multiply branched tree with different macromolecular sequences at vertices. Each line joins neighboring sequences whose values are within 0.5 of locally optimum sequence at lower center for linearized fitness function of type 2 [Eqn. (IV.7)] and reference fold that is cruciform, like tRNA, for sequence of length 72. Over 1300 branches shown extending up to 10 mutant shells away from central optimum. Better sequence (labeled optimum) was found in tenth mutant shell. Non-random sampling of mutant sequences demonstrated typical of population sampling in quasispecies model. Note small number of ridges that penetrate deeply into surrounding mutant space. (Additional connected paths due to hypercube topology of mutant space not shown.)...

To quantify the amount of the resulting ice phase from diffraction data a proper description of these defective ice phases is needed. Here we present a way to fit the diffraction peak profiles with different models of stacking disorder. This may allow us to distinguish different samples with different histories in terms of their stacking distributions. An adapted range of sufficiently large unit cells with different, non-random stacking sequences is created for each sample and a linear combination of these replicas is fitted to the measured neutron diffraction data. In this way a quantitative determination of the total amount of ice present can be obtained. 

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