Dynamic titration methods

The pK found in this way may be directly compared with Forster-cycle calculations. However, straightforward utilization of the fluorescence titration method is usually limited to moderately strong photoacids due to partial deactivation processes of the photoacid occurring in very concentrated mineral acid solutions. The most accurate method of finding the pK of a photoacid is by direct kinetic measurements of the excited-state proton dissociation and recombination rates °. However, these measurements are not trivial and are limited to a relatively small number of photoacids where accurate measurement of the excited-state reversible dynamics of the proton-transfer reaction is possible. 

Frycdk, P, Schug, K.A. (2009) High throughput multiplexed method for evaluation of enantioselective performance of chiral selectors by HPLC-ESI-MS and dynamic titration cinchona alkaloid carbamates discriminating N-blocked amino acids. Chirality, 21, 929-936. 

The Forster cycle and the fluorescence titration methods assume that the dynamic equilibrium between prototropic species is established in the excited state. When fast proton-induced fluorescence quenching (k ) competing with proton transfer process (k ) is involved (see Scheme 2.1), dynamic analysis as described below is required to determine the accurate pK values. 

An alternative formalism to the acidostat method, continuous constant pH molecular dynamics (CPHMD), has been developed by Brooks and coworkers [42, 58] drawing on the flavor of the early work by Mertz and Pettitt [67], In CPHMD, each titration residue carries a titration coordinate, A j, which is a function of an unbounded variable 0j,... 

The titration coordinates evolve along with the dynamics of the conformational degrees of freedom, r, in simulations with GB implicit solvent models [37, 57], An extended Hamiltonian formalism, in analogy to the A dynamics technique developed for free energy calculations [50], is used to propagate the titration coordinates. The deprotonated and protonated states are those, for which the A value is approximately 1 or 0 (end-point states), respectively. Thus, in contrast to the acidostat method, where A represents the extent of deprotonation, is estimated from the relative occupancy of the states with A 1 (see later discussions). The extended Hamiltonian in the CPHMD method is a sum of the following terms [42],... 

For the determination of the dissociation constant in the excited state, several methods have been used the Forster cycle,(109 m) the fluorescence titration curve/113 the triplet-triplet absorbance titration curve,014 but all involve the assumption that the acid-base equilibrium may be established during the lifetime of the excited state, which is by no means a common occurrence. A dynamic analysis using nanosecond or picosecond time-resolved spectroscopy is therefore often needed to obtain the correct pK a values.1(n5)... 

The first electrochemical studies of Mb were reported for the horse heart protein in 1942 (94) and subsequently for sperm whale Mb (e.g., 95) through use of potentiometric titrations employing a mediator to achieve efficient equilibriation of the protein with the electrode (96). More recently, spectroelectrochemical measurements have also been employed (97, 98). The alternative methods of direct electrochemistry (99-102) that are used widely for other heme proteins (e.g., cytochrome c, cytochrome bs) have not been as readily applied to the study of myoglobin because coupling the oxidation-reduction eqiulibrium of this protein to a modified working electrode surface has been more difficult to achieve. As a result, most published electrochemical studies of wild-type and variant myoglobins have involved measurements at eqiulibrium rather than dynamic techniques. 

The two variables change their role with respect to their dependent versus independent, intensive versus extensive nature. This is also true of e.g. calorimetric, conductometric and spectrophotometric titrations using UV-, IR- or NMR-spectrosco-py We additionally have to consider that in the titration of the catalytic process only the external dynamics are measured a direct comparison with the actual metal fraction of the related intermediate complexes is generally not possible We call this analysis of homogeneous catalytic systems by a metal-ligand titration the method of inverse titration and for the resulting diagrams we use the term li nd-concentration control maps ([L]-control maps) . 

The effects of moisture content in drug substances iancthed dosage form have been widely studied. Static moisture content can be determined by many methods like Karl Fisher titration, loss on drying (LOD), and TGA. Dynamic hygroscopicity of a drug substance has beerLcWaato four... 

Sampling of the biomolecular conformations is usually performed using MD simulations or Monte Carlo methods (61, 62). The protonation state of titrateable amino acids can be treated with constant pH dynamics, QM/MM calculations, or continuum electrostatics methods (61, 62). Formation of a protein-protein encounter complex is often studied using Brownian dynamics (63). Studies of protein-protein docking involve electrostatic potential analysis and, more recently, protein flexibility models, for example normal mode analysis (64). 

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