Noncooperative transition

Calorimetric studies have been made on proteins S4, S7, S8, S15, S16, S18, Lll, and L7 (Khechinashvili et al., 1978 Gudkov and Behike, 1978). Most of these proteins displayed a cooperative tertiary structure in solution. Proteins S4, S7, SI5, and SI8 were extracted from the ribosome by a urea-LiCl technique followed by renaturation, whereas proteins S8, S16, and Lll were prepared by the mild isolation method. A calorimetric study on protein SI showed a noncooperative transition around 70-80 C, suggesting a flexible tertiary structure (L. Giri, unpublished). 

Similarly, this expression is equivalent to the probabihty of observing any state j in the two-state noncooperative transition. Knowing the probability of a random walk of N steps with j steps forward, the average number (mean value), and the mean of the square of the number, [Pg.272]

Conceptually and mathematically, the one-dimensional random walk is equivalent to the two-state noncooperative transition, with a forward step being one state and the backward step being the second state for each residue. 

The inclusion of cholesterol disturbs the crystalline structure of the gel phase, and the phospholipid chains are more mobile than in its absence. This prevents the crystallization of the hydrocarbon chains into the rigid crystalline gel phase. In the more fluid liquid crystalline phase, the rigid cholesterol molecules restrict the movement of the hydrocarbon chains. In consequence, the addition of cholesterol to lipid bilayers or lamellar mesophases gradually diminishes the gel-liquid crystal transition temperature and the enthalpy and broadens the DSC transition peak [72,73]. No transition can be detected by DSC at 50% cholesterol [73,74] (curve/of Fig. 7), which is the maximum concentration of cholesterol that can be incorporated before phase separation. However, laser Raman spectroscopic studies show that a noncooperative transition occurs over a very wide temperature range [75]. 

Figure 8.15. Bis for the model of Section 8.8, with parameters given in Eq. (8.8.10), and m = 10. The curves from left to right correspond to increasing values of Xg = 0,5,10,15,..., 40. Note the transition from the noncooperative BI for = 0 to a highly (positive and homotropic) cooperative curve for...

The temperature dependence of the chemical shifts of the base and sugar resonances of poly(dA-dT) in 0.1 M phosphate buffer is plotted in Figure 3. There are upfield and downfield shifts associated with the noncooperative premelting transition between 5 and 55°C while only downfield shifts are observed for most of the base and sugar protons on raising the temperature above 65°C in the noncooperative postmelting transition temperature range. 

Rn Semiconductor metal transition occurs at 150°K (cooling), at 180°K (heating). The resistivity changes through the transition by a factor of 10. The low-temperature phase is monoclinic. A noncooperative, high temperature transition occurs over the temperature range 110°C < T < 260°C. 

The complexity of the SC membrane hinders such definitive interpretation, but, nevertheless, alterations in endotherms can be used to screen molecules suspected of altering membrane function. Conversely, one should note that the absence of additive-induced alterations in the phase transition profile does not rale out their perturbing effect, but rather indicates that the additive does not modify the gel phase. As described earlier, a DSC thermogram of hydrated but untreated human SC yields four endotherms, the first three of which can be identified as noncooperative lipid-associated phase transitions, while the high-temperature endotheim is attributed to keratin denaturation [33,37]. 

From the ratio AHyu/AHcai, the cooperative unit size (CUS) (in molecules) can be determined. The CUS is a measure of the degree of intermolecular cooperation between phospholipid molecules in a bilayer for a completely cooperative, first-order phase transition of an absolutely pure substance, this ratio should approach infinity, whereas for a completely noncooperative process, this ratio should approach unity. Although the... 

It may be mentioned here that a recent study (Vasconcelos 1996) of a simple noncooperative (one-block) model of stick-slip motion (described by eqn (4.2) with / o = 0 or eqn (4.4) with k = 0) shows discontinuous velocity-dependent transition in the block displacement, for generic velocity-dependent friction forces. Naive generalisation of this observation for the coupled Burridge-Knopoff model would indicate a possible absence of criticality in the model. 

Finally, we have not observed a spontaneous transition from a low flux to a high flux state (Figure 24.7 A) with our previous MR-based membranes [3,5]. The fact whether this transition is observed depends on the feed concentration suggests that the transition is a transport-related phenomenon. It is possible that this transition relates to the concept of cooperative (high flux) vs. noncooperative (low flux) dehybridization (Figure 24.9), but further studies, both experimental and modeling, will be required before a definitive mechanism for this transition can be proposed. 

Transitions with the native state are slow and cooperative, those with the unfolded state fast and noncooperative. 

Advantages of Hill Plots - Hill plots readily identify the transition between binding states in cooperativity, and the binding behavior is unmistakably different for cooperative and noncooperative systems. Furthermore, the Hill plot gives a direct numerical measure of the degree of cooperativity from its maximum slope, n which is called the Hill coefficient. 

In the noncooperative model (Figure 9.1), the biomacromolecule converts stepwise from a to b, with an increase in the fraction of b with each transition. Each step j represents a different state j with wy being the statistical weight in which j also represents the total number of residues in b conformation with the probability, s = [h]/[a]. There are N unique combinations, i.e. degeneracy with a single residue b for a chain of N residues, therefore wi = Ns and Wy = gys. The general form of the partition function for N number of residues is the polynomial expression ... 

Most transitions in the secondary structures of biomacromolecules fall somewhere between the cooperative none-or-all and the noncooperative models. Many of these transitions can be described by the zipper model, which dissects the structural transition of a polymeric chain into a number of discrete steps (Figure 9.1). The model is a special case of the cooperative structural transition of biomacromolecules. In the zipper model, the initiation of the transition is harder than extension (propagation) and therefore low probability. This initiation step is of high energy and provides a nucleation point for the transition. The subsequent extension steps occur by a series of lower energy and consequently higher probability. 

The partition function for the zipper model is derived from the basic relationships of the noncooperative model. The only difference is the statistical weight for the first step Wi that must include a nucleation parameter, a to represent the probability (lower probability therefore a < 1) for initiating the transition. Therefore the statistical weight for the state / = 1 is w, = as. Two possibilities exist for the next step of the transition. In one case,... 

This is equivalent to the degeneracy of each state in the noncooperative structural transition for the two-state model. The probability of having j forward steps and therefore N - y backward steps, P, is... 

In contrast to iron(II) spin-state crossover complexes which usually show a cooperative behavior, iron(III) complexes exhibit a gradual, noncooperative, spin-state transition. There has been extensive Mossbauer spectral studies of these transitions, including ambient and high-pressure studies of the iron(III) trisdithiocarbamate complexes, the first iron complexes which were reported " in 1931 to undergo a spin-state transition. 

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