Two-state transition

The second test is that the sum of the forward and reverse m values must equal the m value for equilibrium unfolding for a two-state transition that is,... 

The third test is deviations from the simple V-shaped curves of rate constants versus [denaturant] that were shown in Figure 18.1 for CI2. An intermediate was detected from the denaturant dependence of the single phase for the folding of bamase (Figure 18.6) because of downward curvature. This is sometimes called rollover. The rate constant for folding for the two-state transition for bamase can be calculated as a function of [urea] from the equilibrium and rate constants... 

The first is that the enthalpy of unfolding of a protein changes significantly with temperature. Consider that the protein denatures reversibly according to a simple two-state transition in which the denatured state D is in equilibrium with the native structure N. Then, according to classical thermodynamics, the value of A//d n at a temperature T2 (i.e., A//D N(7-2)) is related to that at another temperature T (A//d n(7 1)) by... 

A two-state transition is usually identified by all spectroscopic probes changing simultaneously as the equilibrium changes. The far ultraviolet circular dichroism signals, which are a measure of secondary structure, should change in parallel with the near ultraviolet, which are a measure of tertiary structure. Fluorescence and near ultraviolet absorbance spectra also probe tertiary structure and should change in parallel with each other and the circular dichroism spectra. Ideally, there should be isosbestic or isodichroic points where spectra converge. 

Intermediates are usually detected in reaction pathways by the appearance of additional phases. Most small proteins have only one non-proline-related folding phase in the accessible time range. But the simple kinetics can be deceptive, and there can be hidden intermediates, besides the high energy states discussed in the last section. In Chapter 17, section A4, procedures were described to test for equilibrium two-state transitions these procedures are also effective for detecting intermediates that may accumulate close to the transition region. Simitar tests, such as the simultaneous change of tryptophan fluorescence or near... 

Both the denaturation process in proteins and the melting transition (also referred to as the helix-to-coil transition) in nucleic acids have been modeled as a two-state transition, often referred to as the all-or-none or cooperative model. That is, the protein exists either in a completely folded or completely unfolded state, and the nucleic acid exists either as a fully ordered duplex or a fully dissociated monoplex. In both systems, the conformational flexibility, particularly in the high-temperature form, is great, so that numerous microstates associated with different conformers of the biopolymer are expected. However, the distinctions between the microstates are ignored and only the macrostates described earlier are considered. For small globular proteins and for some nucleic acid dissociation processes,11 the equilibrium between the two states can be represented as... 

Solutions at concentrations above the cmc may contain significant concentrations of both monomeric and micellar surfactant. Previous researchers have used FT-IR to investigate monomer-to-micelle transitions (27) and gel-to-liquid crystal transitions of lipid bilayers (28,29). These studies have demonstrated that, in the case of such two-state transitions, linear combinations of the infrared spectra of the initial and final states characterize the spectra of the intermediate states, where both forms coexist. However, changes in band frequency or width are not necessarily linear with the extent of the transition. Linear combinations of two highly overlapped Lorenztion bands can give rise to non-linear shifts in the band frequency and width (27-29). 

As seen in Fig. 10, the model accurately predicts the presence, location, and area of the cold and heat denaturation peaks. Under these conditions, the hierarchical partition function predicts a heat denaturation peak centered at 58°C and a cold denaturation peak centered at 4°C. The enthalpy change for the heat denaturation peak is 59 kcal mol-1 and the ACp is equal to 2.45 kcal K-1 mol-1. The experimental values reported by Privalov et al. (1986) are 57.5 and 3°C for the heat and cold denaturation transition temperatures, 53 kcal mol-1 for the enthalpy change, and 2.5 kcal K-1 mol-1 for ACp. Analysis of the theoretical curve indicates that it corresponds to a two-state transition, in agreement with the experimental data. The population of partially folded intermediates is never greater than 10-5 during the heat denaturation transition. 

For this simple two-state transition, the traditional deterministic chemical kinetics (see Chapter 3) is based on rate equations for the concentration of A ... 

The solution to Equation (11.37) can be obtained in two parts. From the two-state transition R = mRNA R it follows that the duration between two bursts of protein synthesis is exponentially distributed with mean time 1 / ,. The duration of each burst is also exponentially distributed with mean time 1 / k2. Thus the X in Equation (11.35) is related to the kinetic constant A = k. ... 

These results are extremely informative, but it may well be that even simpler and more direct correlations can be made by relating the effective expansion process to the temperature above the melt temperature for any mix, since this correlates directly with the steam pressure and with thermal reduction of the rheology of the melt. The TJ NatsT content line should ideally be derived for material at the die exit rather than for the raw materials, since the effects of dextrinisation or particulate dispersion in the barrel would not be present in the raw materials. This can be done quite simply by measuring pretreated mixes. However, the fact that measurements of two state transitions (glassy and melting) of a formulation, one prior to extmsion and the second after it, are sufficient to predict raw material performance is remarkable, and deserves to be tested widely on other materials. 

Additionally, we would expect a lipid melting transition to be accompanied by a change in the degree of molecular order and hence accompanied by a change in entropy. For a reversible two-state transition, T represents the temperature at which both phases are in equilibrium and hence the free energy change (AG) associated with the process is zero. The expression... 

W.E. Werner and H.K. Schachman. 1989. Analysis of the ligand-promoted global conformational change in aspartate transcarbamoylase Evidence for a two-state transition from boundary spreading in sedimentation velocity experiments J. Mol. Biol. 206 221-230. (PubMedl... 

Two-state transitions under similar conditions were also observed for human PrP(91-231) (Jackson et al, 1999b Hosszu et at., 1999) and human PrP(90-231) (Swietnicki et al, 1997 Swiemicki et al, 1998). 

The heat capacity peak, characteristic of the transition, reflects the excess heat capacity arising from the enhanced enthalpy fluctuations that occur in the temperature range of the transition. In the case of a two-state transition, the thermodynamic functions are obtained in a straightforward way from the area QD under the peak (corrected for the baseline), which measures the overall enthalpy change resulting from the transition, and the overall heat capacity difference (ACp) ... 

Figure 5.13 General two-state transition curve. The observable F) can be any experimental parameter (heat uptake, fluorescence intensity, UV absorbance, CD intensity, etc.). The variable (x) is whatever is bringing about the transition e.g. temperature, pressure, concentration, pH). The dotted lines give the extrapolated baselines, showing what F would be for the initial or final states in the absence ol any transition...

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