Two-point kinetics

In methods employing two-point kinetics, the enzyme activity is determined by measuring the reflection at two different times. 

Dl = primary reflection density (1st wavelength), t = time (minutes), 

Several reflections are measured within a defined period of time. 

Explanations of abbreviations as for eq. (13), but in this case rate = multiple-point measurement of the reflection referred to the period of measurement. 

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Methods in which some property related to substrate concentration (such as absorbance, fluorescence, chemiluminescence, etc.) is measured at two fixed times during the course of the reaction are known as two-point kinetic methods. They are theoreticahy the most accurate for the enzymatic determination of substrates. However, these methods are technically more demanding than equifibrium methods and all the factors that affect reaction rate, such as pH, temperature, and amount of enzyme, must be kept constant from one assay to the next, as must the timing of the two measurements. These conditions can readily be achieved in automatic analyzers. A reference solution of the analyte (substrate) must be used for calibration. To ensure first-order reaction conditions, the substrate concentration must be low compared to the K, (i.e., in the order of less than 0.2 X K, . Enzymes with high K , values are therefore preferred for kinetic analysis to give a wider usable range of substrate concentration. 

D. Betteridge and B. Fields, Two-Point Kinetic Simultaneous Determination of Cobalt(II) and Nickel(II) in Aqueous Solution Using Flow Injection Analysis (FIA). Fresenius Z. Anal. Chem., 314 (1983) 386. 

A two-point kinetic turbidimetric technique using commercially available monospecific antisera has been used for the determination of immunoglobulins G, A, and M in sera. The accuracy of the method when measuring idiotypic monoclonal proteins is greater than that of the radial diffusion method. 

Carlo-simulations for LI2 superlattice including saddle-point energies for atomic jumps in fact yielded two-process kinetics with the ratio of the two relaxation times being correlated with the difference between the activation barriers of the two sorts of atom. 

There are two points of the cycle at which velocity decreases very rapidly from a high value to zero. To give a.familiar analogy, the van der Pol oscillator for this value of y. behaves not as a decent oscillator but rather as a pneumatic hammer, which idles for some time while the air pressure builds up, delivers a hammer blow, losing its kinetic energy, and then begins a similar half-cycle. 

The gas motion near a disk spinning in an unconfined space in the absence of buoyancy, can be described in terms of a similar solution. Of course, the disk in a real reactor is confined, and since the disk is heated buoyancy can play a large role. However, it is possible to operate the reactor in ways that minimize the effects of buoyancy and confinement. In these regimes the species and temperature gradients normal to the surface are the same everywhere on the disk. From a physical point of view, this property leads to uniform deposition - an important objective in CVD reactors. From a mathematical point of view, this property leads to the similarity transformation that reduces a complex three-dimensional swirling flow to a relatively simple two-point boundary value problem. Once in boundary-value problem form, the computational models can readily incorporate complex chemical kinetics and molecular transport models. 

The only unknowns in these equations are the two fluorescence lifetimes, which considerably reduces the complexity of the problem. Figure 2.3 shows a plot of N versus D for all possible monoexponential decays, and for all possible mixtures of two monoexponential species with lifetimes equal to 2.5 and 1 ns. The half-circle though (0,0) and (0,1) represents the values of N and D that correspond to all possible monoexponential decay kinetics [13, 16, 43], All the values of /V, and D, for a mixture of two species he on a straight line connecting the two points on the half-circle that correspond to the lifetimes of the two species. The offset and the slope of this straight line are given by Eq. (2.21). 

The rate at which reactions occur is of theoretical and practical importance, but it is not relevant to give a detailed account of reaction kinetics, as analytical reactions are generally selected to be as fast as possible. However, two points should be noted. Firstly, most ionic reactions in solution are so fast that they are diffusion controlled. Mixing or stirring may then be the rate-controlling step of the reaction. Secondly, the reaction rate varies in proportion to the cube of the thermodynamic temperature, so that heat may have a dramatic effect on the rate of reaction. Heat is applied to reactions to attain the position of equilibrium quickly rather than to displace it. 

The first term on the right-hand side of (2.61) is the spectral transfer function, and involves two-point correlations between three components of the velocity vector (see McComb (1990) for the exact form). The spectral transfer function is thus unclosed, and models must be formulated in order to proceed in finding solutions to (2.61). However, some useful properties of T (k, t) can be deduced from the spectral transport equation. For example, integrating (2.61) over all wavenumbers yields the transport equation for the turbulent kinetic energy ... 

Shown in Fig. 7.2 is the relationship between qr and qL for various initial pressures, a value of the heat transfer coefficient h, and a constant wall temperature of In Eq. (7.8) qr takes the usual exponential shape due to the Arrhenius kinetic rate term and cp is obviously a linear function of the mixture temperature T. The qt line intersects the qr curve for an initial pressure l at two points, a and b. 

Polymeric micelles with selected chemistries and molecular architecture of block copolymers, such as PIPAAm-CigHgs, PIPAAm-PSt, PIPAAm-PBMA, and PIPAAm-PLA micelles, showed the same LCST and the same thermoreponsive phase transition kinetics as those for PIPAAm irrespective of the hydrophobic segment incorporation. This confirms two points (a) that hydroxyl groups or amino goups of PIPAAm termini completely react with the hydrophobic segment end groups and (b) that the block copolymers form core-shell micellar structures with hydrophobic iimer cores completely isolated from the aqueous phase. 

The energy of the electron gas is composed of two terms, one Hartree-Fock term (T)hp) and one correlation term (Hartree-Fock term comprises the zero-point kinetic energy density and the exchange contribution (first and second terms on the right in equation 1.148, respectively) ... 

These factors do not argue against the complex-decomposition mechanism, but they should not be too readily interpreted, in the absence of other evidence, as evidence against the sulphide mechanism. Granted, this is an old study, but it does point up the difficulty in distinguishing between the two mechanisms. Kinetic studies and subsequent fitting of the data from these studies to various models [48,49] appear to be the best way of approaching this problem at present. 

Swelling of Spherical Gels. Let us examine kinetics of the macroscopic instability at K = 0 in more details in a spherical gel with radius R immersed in solvent at zero osmotic pressure [18, 21, 46-49]. This should be appropriate because previous theories made no clear distinction between the two points, K = 0 and K + p = 0 [46-48]. The gel expands isotropically and the displacement vector u is assumed to be of the form,... 

Before leaving the discussion of kinetics, two points concerning the experimental determination of reaction orders should be noted. First, the kinetics of surface reactions, in contrast to those of homogeneous systems, are temperature-dependent. This must be the case since the relative surface coverages of the reactants A and B are... 

Two points may be made at this stage. First, the quantity of charge transferred between phases in order to establish an equilibrium potential difference is normally so small that the actual change in composition of the solution is negligible. For example, one can show that when a 1 cm2 platinum electrode is immersed in a Fe2+/Fe3+ solution, a net reduction of between 10-9 and 10-,° moles of Fe3+ takes place. Second, and as will be stressed later, the kinetics of the charge transfer process are very important, since if rates are slow, it may not be possible for a true equilibrium to be established. 

A. Establish the point kinetics and equilibrium isotherm for the adsorption step at the site, and the rate coefficients for the various space processes. These are the two types of data required for design. To some extent estimates may be made for the coefficients for the space processes. 

Equations (6.15) and (6.17) phenomenologically describe the overall growth kinetics after the initial nucleation took place and further nucleation is still occurring. Indeed, the sigmoidal form of the X(t) curve represents a wide variety of transformation reactions. Equation (6.13) is named after Johnson, Mehl, and Avrami [W. A. Johnson, R. E Mehl (1939) M. Avrami (1939)]. Let us finally mention two points. 1) Plotting Vin (1 -X) vs. t should give a straight line with slope km. 2) The time ty of the inflection point (d2X/dt2 = 0) on X(t) is suitable to derive either m or km, namely... 

The direct consequence of this statement for Kirkwood s superposition approximation is as follows. Substitution of equation (2.3.62) into p2,i yields correct order of its magnitude, a 1, provided f] — rfl < ro, r% — r[ > ro (i.e., there is a single A in the recombination sphere around B), since two-point density p p(f, r[ t) oc and pi,i (r 2i t) oc (<7o)° (i.e., is limited as well as another density />2,o> which does not fall into category of virtual configurations). On the other hand, for coordinates satisfying ri - f[ < ro, r 2 — rj < ro (i.e., defect B has in its recombination sphere two defects A) substitution of equation (2.3.62) results in p p oc instead of the correct M Due to this the superposition approximation neglects in the limit (To oo a number of terms in equations which finally leads to a considerable error in the accumulation kinetics. 

Chyraotrypsin inhibitor 2 (CI2) folds rapidly by simple two-state kinetics that is, D N, with a r1/2of 13 ms.18,19 CI2 is a small 64-residue protein that has all its peptidyl-proline bonds in the favorable trans conformation.20 (There are, of course, additional slow cis —> trans peptidyl-prolyl isomerization events, which account for about 20-30% of the refolding amplitudes.) The occurrence of two-state kinetics does not prove that there are no intermediates on the folding pathway there could be intermediates that are present at high energy and are kineti-cally undetectable (see section B4). Two-state behavior has subsequently been found for many other small proteins. The simplicity of two-state folding kinetics provides the ideal starting point for the analysis and illumination of the basic principles of folding. 

Let us now consider the problem from the standpoint of calcite precipitation kinetics. At saturation states encountered in most natural waters, the calcite reaction rate is controlled by surface reaction kinetics, not diffusion. In a relatively chemically pure system the rate of precipitation can be approximated by a third order reaction with respect to disequilibrium [( 2-l)3, see Chapter 2]. This high order means that the change in reaction rate is not simply proportional to the extent of disequilibrium. For example, if a water is initially in equilibrium with aragonite ( 2c=1.5) when it enters a rock body, and is close to equilibrium with respect to calcite ( 2C = 1.01), when it exits, the difference in precipitation rates between the two points will be over a factor of 100,000 The extent of cement or porosity formation across the length of the carbonate rock body will directly reflect these... 

However, Costa et al. considered all of them as diffusion-limited [Fig. 3.12(a)]. If the kinetic rate constant is large enough, it could be that the diffusion control of the transfer occurs at rather small and even moderate D. But it is doubtful that the reaction remains diffusional up to the largest D, when Rq becomes smaller than the contact distance ct. This is particularly true for the last two points in the circles (for cyclohexane and hexane). They fall on the horizontal line R = ct if only one assumes that charge transfer in these solvents takes place at collisional distances [16]. 

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