Two-Step-Model

The current understanding on activation of Tec kinases fits into a two-step model. In the first step an intramolecular interaction between the SH3 domain and aproline-rich region in the TH domain is disrupted by binding ofthe PH domain to phosphoinositides, G protein subunits, or the FERM domain of Fak. These interactions lead to conformational changes of Tec and translocation to the cytoplasmic membrane where, in a second step, Src kinases phosphorylate a conserved tyrosine residue in the catalytic domain thereby increasing Tec kinase activity. Autophosphorylation of a tyrosine residue in the SH3 domain further prevents the inhibitory intramolecular interaction resulting in a robust Tec kinase activation. 

Two-step models, which first solve mass momentum and energy balances for each time step and then reequilibrate the chemistry using a distribution-of-species code. 

FIG. 6. (A) A two step model for the sequential loss of sister chromatid cohesion in animal... 

The above TGA and elemental analysis studies are consistent with Van Krevelen s two step model for polymer charring (2) in which a polymer first rapidly decomposes at 500°C to fuel gases and a primary char residue characterized by modestly high hydrogen content. On further heating above 550°C, this primary char is slowly converted in a second step to a nearly pure carbon residue by the loss of this hydrogen. 

Because this reaction must involve two steps, diffusion of selenate into the interlayer spaces of the green rust followed by electron transfer from Fe(ll) green rust, Johnson and Bullen (2003) interpreted this result using a two-step model similar to that discussed above. The diffusion step presumably has very little isotopic fractionation associated with it. Step 2 might be expected to involve a kinetic isotope effect similar to that observed in the HCl reduction experiments. As is discussed above, if the diffusion step is partially rate-limiting, the isotopic fractionation for the overall process should be less than the kinetic isotope effect occurring at the reduction step. This appears to be the case, as the ese(vi)-se(iv) value of 7.4%o is somewhat smaller than that observed for reduction by strong HCl (12%o). 

Figure 10. Fe isotope compositions for total aqueous Fe (Fe,(,T) and ferrihydrite (FH) precipitate and aqueous Fe-ferrihydrite fractionations from the batch oxidation and precipitation experiment of Bullen et al. (2001). (A) Measured S Fe values from Bullen et al. (2001), compared to simple Rayleigh fractionation (short-dashed lines, noted with R ) using 10 1naFe.,-FH = 0.9%o, as well as the two-step re-equilibration model discussed in the text (i.e., Eqn. 12), shown in solid gray lines for the aqueous Fe and ferrihydrite components the predicted 5 Fe value for Fe(III), is shown in the heavy dashed line, which reflects continual isotopic equilibrium between Fe(II), and Fe(III),(. Note that in the experiment of Bullen et al. (2001), aqueous Fe existed almost entirely as Fe(II),(,. (B) Measured fractionation between total aqueous Fe and ferrihydrite precipitate, as measured, and as predicted from simple Rayleigh fractionation (black dashed line) and the two-step model where isotopic equilibrium is maintained between aqueous Fe(II),q and Fe(III),q (solid gray line).

The data of Croal et al. (2004) may also be interpreted to reflect a two-step proeess, where a -2.9%o fractionation occurs between Fe(ll)aq and Fe(lll)aq, accompanied by a +1.4%o fractionation between Fe(lll)aq and ferrihydrite upon precipitation, produces a net fractionation of-1.5%0. When cast in terms of common mechanistic models for separation of solid and liquid phases such as Rayleigh fractionation, it becomes clear that the two-step model produces essentially the same fractionation trend as a single -1.5%o fractionation step between Fe(ll)aq and ferrihydrite if the Fe(lll)aq/Fe(ll)aq ratio is low (Fig. 14). As the Fe(lll)aq/Fe(ll)aq ratio inereases, however, the calculated net Fe(ll)aq-ferrihydrite fractionation in the two-step model deviates from that of simple Rayleigh fractionation (Fig. 14). Unfortunately, the scatter in the data reported by Croal et al. (2004), which likely reflects minor contamination of Fe(ll)aq in the ferrihydrite precipitate, prevents distinguishing between these various models without eonsideration of additional factors. 

Finally, the novel part of the three-step model is the identification of a separate unit operation (subsystem) in a PBC system, that is, the thermochemical conversion of the fuel bed, which by logical consequence requires the introduction of a third subsystem referred to as the conversion system. Commonly, PBC systems are modelled with two steps, that is, a two-step model [3,15], see Figure 7. In the two-step model the thermochemical conversion of solid fuels and the gas-phase combustion are lumped together. Several new concepts are deduced in the scope of the three-step model in general and the conversion system in particular, for example the conversion gas, conversion concept, conversion zone, conversion efficiency, which are all explained later in this summary. 

What the three-step model really points out is that it is theoretically correct to carry out basic combustion calculations for a PBC system based on the mass flow and stoichiometry of the conversion gas from the conversion system and not based on the mass flow of solid fuel entering the conversion system. The two-step model approach applied on a PBC system, which is equivalent to assuming that the conversion efficiency is 100 %, is a functional engineering approach, because the conversion efficiency is in many cases very close to unity. However, there are cases where the two-step model approach results in a physical conflict, for example the mass flows in PBC sysfem of batch type cannot be theoretically analysed with a two-step model. 

Very often in the literature, the physical model used to describe a PBC system is a two-step model [18,19] that is, the conversion system and the combustion system are regarded as one unit referred to as the combustion system (combustion chamber, furnace), see Figure 14. The two-step model is based on the assumption that the conversion system is ideal that is, the conversion efficiency [3] is 100%, which is not the case in real solid-fuel fired systems. However, the two-step model is a functional engineering approach. 

The main isotope-discriminating steps during biological carbon fixation are (1) the uptake and intracellular diffusion of CO2 and (2) the biosynthesis of cellular components. Such a two-step model was first proposed by Park and Epstein (1960) ... 

From this simplified scheme, it follows that the diffusional process is reversible, whereas the enzymatic carbon fixation is irreversible. The two-step model of carbon fixation clearly suggests that isotope fractionation is dependent on the partial pressure of CO2, i.e. PCO2 of the system. With an unlimited amount of CO2 available to a plant, the enzymatic fractionation will determine the isotopic difference between the inorganic carbon source and the final bioproduct. Under these conditions, C fractionations may vary from -17 to —40%o (O Leary 1981). When the concentration of CO2 is the limiting factor, the diffusion of CO2 into the plant is the slow step in the reaction and carbon isotope fractionation of the plant decreases. 

Since Eqs. 11 and 12 are not of the same type, the reaction evidently is nonelemen-tary. Consequently, let us try various mechanisms and see which gives a rate expression similar in form to the experimentally found expression. We start with simple two-step models, and if these are unsuccessful we will try more complicated three-, four-, or five-step models. 

Figure 6.4 Schematic of the two step model and the categories of physicochemical tools. (Adapted from [3]).

Fig. 7. Deactivation of CPCR in microemulsion Marlipal 013-60/Water/Cyclohexane at y = 0.1 and Wq = 5 following the two-step-model (solid line). The one-step-model (dotted line) does not fit the experimental results appropriately...

According to Kennedy et aL (1980), these observations suggest that the transformed clones do not occur as the direct consequence of carcinogen treatment. Rather, these authors propose a two-step model to explain the results. The initial change induced by the carcinogen apparently occurs in a large number, perhaps all, of the cells. This change does not result directly in the transformation of the cells but increases the probability of their transformation as a rare, secondary event (Kennedy, 1984). 

The relatively simple spectral and kinetic behavior of 10-CPT in methanol-water mixtures can be described by a well-developed reversible diffusion influenced two-step model (Scheme 1). We successfully applied this scheme in the experimental and theoretical studies of reversible ESPT processes in solution. 

The contribution of electrostatic interactions to fast association was analyzed by applying the classical Debye-Hiickel theory of electrostatic interactions between ions to mutants of bamase and barstar whose ionic side chains had been altered by protein engineering (Chapter 14).16 The association fits a two-step model that is probably general (equation 4.84). 

The power-time data obtained for the hydrolysis reactions were fitted to Eq. (7) to determine the values of the reaction parameters. A typical fit line is represented in Figure 4. The data were also fitted to the simpler Eq. (6) Figure 5). This showed whether the models possessed sufficient sensitivity to determine mechanistic information. It is apparent that the simpler model did not fit the experimental data as well as the more complex model, indicating that the data do indeed reflect a three-step process. The two-step model gives a reasonable fit over the initial section of data, where the first two hydrolysis reactions predominate, but cannot fit the section of data where all three hydrolyses are occurring. 

Muller, D., Bitter, F., Kasche, J. and Muller, B. (2005) A two step model for the assessment of the indoor air quality. Proceedings of the 10th International Conference on Indoor Air Quality and Climate, Indoor Air 2005, Beijing, China, Vol. I (1), pp. 20-5. 

An example of a two-site model for pesticide desorption kinetics from soils was presented by McCall and Agin (1985). Using a reversible first-order equation to describe picloram desorption from soil, the authors plotted ln(CB - CBeq) versus t, where CB is the bound form of picloram and CBeq is the bound form at equilibrium, in Fig. 9.4. It is obvious that desorption conforms to a two-step process where a fast step occurs for about a 5-h period, and then a slow process as shown from the linear portion of Fig. 9.4 occurs from 5 to 300 h. McCall and Agin (1985) used the following two-step model to describe the data shown in Fig. 9.4 ... 

The second class consists of processes which can be described in a two-step model by an inner-shell excitation or ionization process followed by a subsequent... 

Within the two-step model for photoionization and subsequent Auger decay, the kinetic energy of Auger electrons for normal (diagram) transitions comes from the energy difference of the ion states before (subscript i) and after (subscript f) the Auger decay, i.e.,... 

Within the two-step model, one can say that the intermediate photoionized state is the initial state for the Auger transition. For the K-LL spectrum of neon this initial state is described by ls2s22p6 2Sj/2. For the final state the possible electron configurations of the ion were shown in Fig. 2.5. Within the LS-coupling scheme which applies well to neon, these electron configurations yield the following final... 

In addition, the observed width of an Auger line is also affected by the spectrometer resolution. However, the bandpass of the incident radiation which produces the initial state for the Auger decay does not play a role, unlike in the case of the width of an observed photoline. (This statement only holds for the two-step model of inner-shell ionization and subsequent Auger decay. In the vicinity of the inner-shell ionization threshold it significantly fails due to postcollision interaction (Section 5.5) and the resonant Raman Auger effect (Section 5.1.2.1).) Hence, Auger transitions often appear in the spectra of ejected electrons as lines much sharper than the corresponding photolines. 

As a consequence of the two-step model for photoionization and subsequent Auger decay, there is a factorization of all observables. For the intensity, the product between the photoionization cross section Auger yield oja has already been discussed in connection with equ. (3.22), and for the angular distribution parameter fiA one has [BKa77]... 

As a special application of the two-step model the non-coincident observation of photon-induced Auger electron emission will be considered further. In this case one has to integrate the transition rate P of equ. (8.66a) over dKa, because the photoelectron is not observed, i.e.,... 

In these expressions the indices fc2 and k1 are restricted to even values (cf. equ. (8.97b)), because in the two-step model single photoionization and Auger decay are treated separately. 

Tashiro A, Dunaevsky A, Blazeski R, Mason CA, Yuste R (2003) Bidirectional regulation of hippocampal mossy fiber filopodial motility by kainate receptors a two-step model of synaptoge-nesis. Neuron 38 773-84... 

A similar equation has been derived20 from a two-step model in which the CaO is assumed to be formed first in some active state CaO which occupies a constant fraction of the surface. The reactions then are... 

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