Crossing over

It has to be emphasized here that in order to study mitotic crossing-over certain precautions have to be taken. First, extended incubation of diploid yeast cells in buffer might induce sporulation and consequently lead to the expression of recessive markers. A control sample which shows an increase of mitotic recombination, especially in acetate buffers, indicates induction of meiosis. To avoid this, one has to shorten the time of treatment and use another buffer. 

Mitotic crossing-over is usually detected by the appearance in a heterozygous strain of recessive markers, either a recessive resistance marker or adel or ade2 red adenine mutant alleles. The mere observation 

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The polymers described so far have relatively flexible main chains which can result in complex confonnations. In some cases, tliey can double back and cross over tliemselves. There are also investigations on polymers which are constrained to remain in a confonnation corresponding, at least approximately, to a straight line, but which have amphiphilic properties tliat ensure tliat tliis line is parallel to tire water surface. Chiral molecules are one example and many polypeptides fall into tliis class [107]. Another example is cofacial phtlialocyanine polymers (figure C2.4.9). 

An alternative mechanism of excess energy release when electron relaxation occurs is through x-ray fluorescence. In fact, x-ray fluorescence favorably competes with Auger electron emission for atoms with large atomic numbers. Figure 16 shows a plot of the relative yields of these two processes as a function of atomic number for atoms with initial K level holes. The cross-over point between the two processes generally occurs at an atomic number of 30. Thus, aes has much greater sensitivity to low Z elements than x-ray fluorescence. 

Knots nd Ca.tena.nes, Closed-circular DNA hehces can cross over one another three or more times to form topological knots. These stmctures are not common, but have been found to occur naturally in some bacteriophage DNAs. 

Styrene Copolymers. Acrylonitrile, butadiene, a-methylstyrene, acryUc acid, and maleic anhydride have been copolymerized with styrene to yield commercially significant copolymers. Acrylonitrile copolymer with styrene (SAN), the largest-volume styrenic copolymer, is used in appHcations requiring increased strength and chemical resistance over PS. Most of these polymers have been prepared at the cross-over or azeotropic composition, which is ca 24 wt % acrylonitrile (see Acrylonithile polya rs Copolyp rs). 

The experimental studies of a large number of low-temperature solid-phase reactions undertaken by many groups in 70s and 80s have confirmed the two basic consequences of the Goldanskii model, the existence of the low-temperature limit and the cross-over temperature. The aforementioned difference between quantum-chemical and classical reactions has also been established, namely, the values of k turned out to vary over many orders of magnitude even for reactions with similar values of Vq and hence with similar Arrhenius dependence. For illustration, fig. 1 presents a number of typical experimental examples of k T) dependence. 

In the first case the cross-over temperature is given by... 

This means that there is a cross-over temperature defined by (1.7) at which tunneling switches off , because the quasiclassical trajectories that give the extremum to the integrand in (2.1) cease to exist. This change in the character of the semiclassical motion is universal for barriers of arbitrary shape. 

Of special interest is the case of parabolic barrier (1.5) for which the cross-over between the classical and quantum regimes can be studied in detail. Note that the above derivation does not hold in this case because the integrand in (2.1) has no stationary points. Using the exact formula for the parabolic barrier transparency [Landau and Lifshitz 1981],... 

Fig. 8. Arrhenius plot of dissipative tunneling rate in a cubic potential with Vq = Sficoo and r jlto = 0, 0.25 and 0.5 for curves 1-3, respectively. The cross-over temperatures are indicated by asterisks. The dashed line shows k(T) for the parabolic barrier with the same CO and Va-...

Friction also changes the way k ) approaches its low-temperature limit and widens the intermediate region between the two asymptotes of k(P). At temperatures far below the cross-over point k T) behaves as... 

Equation (2.41) describes either damped oscillations (at tls < 2do) or exponential relaxation OItls > 2do). Since tls grows with increasing temperature, there may be a cross-over between these two regimes at such that 2h QoJ Ao)coth P hAo) = 2Aq. If the friction coefficient... 

Coupling to these low-frequency modes (at n < 1) results in localization of the particle in one of the wells (symmetry breaking) at T = 0. This case, requiring special care, is of little importance for chemical systems. In the superohmic case at T = 0 the system reveals weakly damped coherent oscillations characterised by the damping coefficient tls (2-42) but with Aq replaced by A ft-If 1 < n < 2, then there is a cross-over from oscillations to exponential decay, in accordance with our weak-coupling predictions. In the subohmic case the system is completely localized in one of the wells at T = 0 and it exhibits exponential relaxation with the rate In k oc - hcoJksTY ". 

This formula, aside from the prefactor, is simply a one-dimensional Gamov factor for tunneling in the barrier shown in fig. 12. The temperature dependence of k, being Arrhenius at high temperatures, levels off to near the cross-over temperature which, for A = 0, is equal to ... 

That is, the exponential increase of the isotope effect with is determined by the difference of the zero-point energies. The cross-over temperature (1.7) depends on the mass by... 

The two-mode model has two characteristic cross-over temperatures corresponding with the freezing of each vibration. Above = hcoo/2k the dependence k(T) is Arrhenius, with activation energy equal to... 

The transition is fully classical and it proceeds over the barrier which is lower than the static one, Vo = ntoColQl- Below but above the second cross-over temperature T 2 = hcoi/2k, the tunneling transition along Q is modulated by the classical low-frequency q vibration. The apparent activation energy is smaller than V. The rate constant levels off to its low-temperature limit k only at 7 < Tc2, when tunneling starts out from the ground state of the initial parabolic term. The effective barrier in this case is neither V nor Vo,... 

It is noteworthy that it is the lower cross-over temperature T 2 that is usually measured. The above simple analysis shows that this temperature is determined by the intermolecular vibration frequencies rather than by the properties of the gas-phase reaction complex or by the static barrier. It is not surprising then, that in most solid state reactions the observed value of T 2 is of order of the Debye temperature of the crystal. Although the result (2.77a) has been obtained in the approximation < ojo, the leading exponential term turns out to be exact for arbitrary cu [Benderskii et al. 1990, 1991a]. It is instructive to compare (2.77a) with (2.27) and see that friction slows tunneling down, while the q mode promotes it. 

This formula, however, tacitly supposes that the instanton period depends monotonically on its amplitude so that the zero-amplitude vibrations in the upside-down barrier possess the smallest possible period 2nla>. This is obvious for sufficiently nonpathological one-dimensional potentials, but in two dimensions this is not necessarily the case. Benderskii et al. [1993] have found that there are certain cases of strongly bent two-dimensional PES when the instanton period has a minimum at a finite amplitude. Therefore, the cross-over temperature, formally defined as the lowest temperature at which the instanton still exists, turns out to be higher than that predicted by (4.7). At 7 > Tc the trivial solution Q= Q Q is the saddle-point coordinate) emerges instead of instanton, the action equals S = pV (where F " is the barrier height at the saddle point) and the Arrhenius dependence k oc exp( — F ") holds. 

However, for these parameters of the barrier, the cross-over temperature would exceed 500 K, while the observed values are 50 K. If one were to start from the d values calculated from the experimental data, the barrier height would go up to 30-40 kcal/mol, making any reaction impossible. This disparity between Vq and d is illustrated in fig. 34 which shows the PES cuts for the transition via the saddle-point and for the values of d indicated in table 2. 

Another eommon eombustion problem eoneerns the erossover tubes. Cross-over tubes are used in ean-annular eombustors to assure eombustion in all ehambers and to equalize pressure. Many times the flow of hot gases through the erossover tubes is inereased due to bloeked fuel nozzles, whieh ean lead to tube failures as shown in Figure 21-17. 

To illustrate how this rather complicated structure is built up, we will start by wrapping a piece of string around a barrel as shown in Figure S.16. The string goes up and down the barrel four times, crosses over once at the bottom and twice at the top of the barrel. This configuration is the basic pattern for the jelly roll motif. 

Like other hormones in this class of cytokines, GH has a four-helix bundle structure as described in Chapter 3 (see Figures 3.7 and 13.18). Two of the a helices, A and D, are long (around 30 residues) and the other two are about 10 residues shorter. Similar to other four-helix bundle structures, the internal core of the bundle is made up almost exclusively of hydrophobic residues. The topology of the bundle is up-up-down-down with two cross-over connections from one end of the bundle to the other, linking helix A with B and helix C with D (see Figure 13.18). Two short additional helices are in the first cross-over connection and a further one in the loop connecting helices C and D. 

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