Bimolecular diffusion constant

The most common quenchers are oxygen, acrylamide, iodide, and cesium ions. The kq value increases with probability of collisions between the fluorophore and quencher. Oxygen is a small and uncharged molecule, so it can diffuse easily. Therefore, the bimolecular diffusion constant kq observed for oxygen in solution is the most important between all cited quenchers. 

We have determined the fluorescence polarization P and the bimolecular diffusion constant fcq of oxygen of the unique Trp residue of a protein at three temperatures, 5, 20, and 30°C, and at two hydrostatic pressures (0-4 kbar), and obtained the following results ... 

Since the intensity average lifetime or the mean lifetime is the average amount of time a fluorophore spends in the excited state, it is normal that this time should be applied to determine the rotational correlation time of a fluorophore, the bimolecular diffusion constant of small molecules such as oxygen, iodide and cesium ions in macromolecules and in energy transfer studies. 

M and a bimolecular diffusion constant of 1.675 0.06 M s. Thus, binding of the glycoprotein to the LCA-FITC complex increases the diffusion of iodide around the fluorescein, i.e. the fluctuations around the probe are more important when STF is bound to the LCA-FITC complex. 

Since the fluorescein is randomly located on the protein surface, the calculated bimolecular diffusion constant is a mean one chai acterizing the mean dynamics of the amino acids of LCA. 

Binding of STF to the LCA-FITC complex induces an increase of the Stern-Volmer and of the bimolecular diffusion constants (k increases from 3.795 M for the LCA-FITC complex, to 5.476 M in presence of STF, and kq increases from 1.16 x 10 to 1.675 x 10 M s ). Thus, the accessibility of iodide to the fluorescein increases and the dynamics of LCA are more important in presence of STF. The more the fluctuations of the protein matrix are important, the more the diffusion of the quencher is facilitated and the more kq is higher. 

X-ray diffraction and fluorescence studies performed on LCA have indicated that the carbohydrate binding site is flexible (Loris et al. 1993). The carbohydrates in LTF and STF are highly flexible (Dauchez et al. 1992). This flexibility is maintained when the glycoproteins are bound to the LCA (Albani et al. 1997). Otherwise, the carbohydrates would not conserve their extended conformation and we should observe a more compact structure between LCA and the glycoproteins, i.e. we should observe a decrease in the bimolecular diffusion constant of KI. 

From these considerations we conclude that diffusion-limited bimolecular rate constants are of the order 10 -10 M s . If an experimentally measured rate constant is of this magnitude, the usual conclusion is, therefore, that it is diffusion limited. For example, this extremely important reaction (in water)... 

A minor component, if truly minute, can be discounted as the reactive form. To continue with this example, were KCrQ very, very small, then the bimolecular rate constant would need to be impossibly large to compensate. The maximum rate constant of a bimolecular reaction is limited by the encounter frequency of the solutes. In water at 298 K, the limit is 1010 L mol-1 s"1, the diffusion-controlled limit. This value is derived in Section 9.2. For our immediate purposes, we note that one can discount any proposed bimolecular step with a rate constant that would exceed the diffusion-controlled limit. 

The rate of MV formation was also dependent on pH. The bimolecular rate constant, as calculated from the first order rate constant of the MV build-up and the concentration of colloidal particles, was substantially smaller than expected for a diffusion controlled reaction Eq. (10). The electrochemical rate constant k Eq. (9) which largely determines the rate of reaction was calculated using a diffusion coefficient of of 10 cm s A plot of log k vs. pH is shown in Fig. 24. 

Mn2(CO)9 reacted with CO at a rate well below the diffusion-controlled limit (77), and the bimolecular rate constant was solvent dependent [It =... 

In liquids, collisional energy transfer takes place by multistep diffusion (the rate determining step) followed by an exchange interaction when the pair is very close. The bimolecular-diffusion-controlled rate constant is obtained from Smoluchowski s theory the result, including the time-dependent part, may be written as... 

The experimental and simulation results presented here indicate that the system viscosity has an important effect on the overall rate of the photosensitization of diary liodonium salts by anthracene. These studies reveal that as the viscosity of the solvent is increased from 1 to 1000 cP, the overall rate of the photosensitization reaction decreases by an order of magnitude. This decrease in reaction rate is qualitatively explained using the Smoluchowski-Stokes-Einstein model for the rate constants of the bimolecular, diffusion-controlled elementary reactions in the numerical solution of the kinetic photophysical equations. A more quantitative fit between the experimental data and the simulation results was obtained by scaling the bimolecular rate constants by rj"07 rather than the rf1 as suggested by the Smoluchowski-Stokes-Einstein analysis. These simulation results provide a semi-empirical correlation which may be used to estimate the effective photosensitization rate constant for viscosities ranging from 1 to 1000 cP. 

Photolysis of DMDAF in benzene containing methyl alcohol gives the ether expected from the reaction of the singlet carbene. Monitoring this reaction by laser spectroscopy reveals that the detected transient reacts with the alcohol with a bimolecular rate constant very near the diffusion limits. In contrast, the transient reacts with triethylamine at least 100 times more slowly than it does with alcohol (Table 7). This behavior is inconsistent with identification of the transient as the cation or radical and points to its assignment as the singlet carbene. 

Using, for example, cyclic voltammetry, the cathodic peak current (normalized to its value in the absence of RX) is a function of the competition parameter, pc = ke2/(ke2 + kin), as detailed in Section 2.2.6 under the heading Deactivation of the Mediator. The competition parameter can be varied using a series of more and more reducing redox catalysts so as eventually to reach the bimolecular diffusion limit. km is about constant in a series of aromatic anion radicals and lower than the bimolecular diffusion limit. Plotting the ratio pc = keij k,n + km) as a function of the standard potential of the catalysts yields a polarogram of the radical whose half-wave potential provides the potential where ke2 = kin, and therefore the value of... 

Where k 1 and k301 are forward and reverse activation-controlled rate cosntants, kd is the ate constant for the diffusion of the fragments out of the solvent cage, and dif is the bimolecular diffusion-limited rate constant. 

By comparing time-resolved and steady-state fluorescence parameters, Ross et alm> have shown that in oxytocin, a lactation and uterine contraction hormone in mammals, the internal disulfide bridge quenches the fluorescence of the single tyrosine by a static mechanism. The quenching complex was attributed to an interaction between one C — tyrosine rotamer and the disulfide bond. Swadesh et al.(()<>> have studied the dithiothreitol quenching of the six tyrosine residues in ribonuclease A. They carefully examined the steady-state criteria that are useful for distinguishing pure static from pure dynamic quenching by consideration of the Smoluchowski equation(70) for the diffusion-controlled bimolecular rate constant k0,... 

Since the rate constants of bimolecular diffusion-limited reactions in isotropic solution are proportional to T/ these data testify to the fact that the kt values are linearly dependent on the diffusion coefficient D in water, irrespective of whether the fluorophores are present on the surface of the macromolecule (human serum albumin, cobra neurotoxins, proteins A and B of the neurotoxic complex of venom) or are localized within the protein matrix (ribonuclease C2, azurin, L-asparaginase).1 36 1 The linear dependence of the functions l/Q and l/xF on x/t] indicates that the mobility of protein structures is correlated with the motions of solvent molecules, and this correlation results in similar mechanisms of quenching for both surface and interior sites of the macromolecule. 

In addition to the partition coefficient, the bimolecular quenching constant (km) is obtained from quenching experiments. 1"1 "7-IIX i and, in principle, this can be used to obtain the lateral diffusion constant of the quencher by using the Smoluchowski equation ... 

Fig. 11 Forward electron transfer (90) rate constant, k, versus the standard potential, F /q, of a series of aromatic anion radicals for rapidly cleaved aryl halide anion radicals (DMF, 20°C). kjy is the bimolecular diffusion limit. (Adapted from Andrieux et al., 1979.)...

Once activated, MV-CCP reacts with 1 equiv of H2O2 in a bimolecu-lar reaction, presumably to form compound 0. In YCCP and HRP this species is referred to as compound ES or compound I, respectively, and contains oxyferryl heme and either a porphyrin n -cation radical (HRP) or an amino acid radical (YCCP). However, the presence of an extra reducing equivalent on the second heme in CCP suggests that such an oxidizing radical species close to the active site heme will be very shortlived and readily form compound I (Fig. 10), which is formally Fe(HI) Fe(IV)=0. The bimolecular rate constant for compound I formation is reported to be very close to the diffusion limit (84). 

Pick s laws describe the interactions or encounters between noninteracting particles experiencing random, Brownian motion. Collisions in solution are diffusion-controlled. As is discussed in most physical chemistry texts , by applying Pick s Pirst Law and the Einstein diffusion relation, the upper limit of the bimolecular rate constant k would be equal to... 

M -sec k The corresponding upper limit value for a bimolecular rate constant in the gas phase is about 10 M -sec k Thus in solutions, bimolecular rate constants cannot exceed 10 -10 M -sec since diffusion control takes over from collision control. 

A reaction whose rate is limited (or controlled) only by the speed with which reactants diffuse to each other. For a ligand binding to a protein, the bimolecular rate constant for diffusion-limited association is around 10 M s. The enzyme acetylcholinesterase has an apparent on-rate constant of 1.6 x 10 M s with its natural cationic substrate acetylcholine, and the on-rate constant of about 6 X 10 with acetylselenoylcholine and about... 

The above models describe a simplified situation of stationary fixed chain ends. On the other hand, the characteristic rearrangement times of the chain carrying functional groups are smaller than the duration of the chemical reaction. Actually, in the rubbery state the network sites are characterized by a low but finite molecular mobility, i.e. R in Eq. (20) and, hence, the effective bimolecular rate constant is a function of the relaxation time of the network sites. On the other hand, the movement of the free chain end is limited and depends on the crosslinking density 82 84). An approach to the solution of this problem has been outlined elsewhere by use of computer-assisted modelling 851 Analytical estimation of the diffusion factor contribution to the reaction rate constant of the functional groups indicates that K 1/x, where t is the characteristic diffusion time of the terminal functional groups 86. ... 

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