Titration dynamic

In molecular mechanics and molecular dynamics studies of proteins, assig-ment of standard, non-dynamical ionization states of protein titratable groups is a common practice. This assumption seems to be well justified because proton exchange times between protein and solution usually far exceed the time range of the MD simulations. We investigated to what extent the assumed protonation state of a protein influences its molecular dynamics trajectory, and how often our titration algorithm predicted ionization states identical to those imposed on the groups, when applied to a set of structures derived from a molecular dynamics trajectory [34]. As a model we took the bovine... 

Wlodek, S. T., Antosiewicz, J., McCammon, J. A. Prediction of titration properties of structures of a protein derived from molecular dynamics trajectories. Protein Sci. 6 (1997) 373-382. 

FIG. 11 Titration plot of alkanesulfonates. Sample 60 wt % of Hostapur SAS 60, monosulfonates fraction contents ca. 140 mg/100 ml (10% MeOH) solution to be titrated 10 ml, 5 ml buffer pH 3 (Merck), 5 ml MeOH, diluted to 100 ml with water titrant 0.004 mol/l TEGOtrant A 100 (l,3-didecyl-2-methyl-imidazolium chloride, Metrohm 6.2317.000) titrator Titrino 716 DMS with automatic titrator 727 and propellant stirrer titration mode dynamic end point titration (DET), high-sense electrode Metrohm 6.0504.15Q, reference electrode Ag/AgCl Metrohm 6.0733.100, EP = end point. 

In ESL, the initial conditions for concentrations A, B, C, and D are followed by the table of measured data, time (min.) versus titrated volume (mL). In the DYNAMIC section, the program statements are identical to those of the model equations. Here, a function generator, FGENl, is used to describe the tabular data. The objective function to be minimised is defined as follows... 

Dynamic measurements (stationary solution). The pH change during one continuous pulse (up to 150 pC) is registered. Owing to the small volume involved, diffusion times have only a limited effect and the recording gives a fair approximation of the titration curve. 

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],... 

Baptista M, Teixeira VH, Soares CM (2002) Constant-pH molecular dynamics using stochastic titration. J Chem Phys 117 4184-4200. 

Lee S, Salsbury FR Jr, Brooks CL III (2004) Constant-pH molecular dynamics using continuous titration coordinates. Proteins 56 738-752. 

Karl Fischer titrators, 23 477 Karmen-vortex street, 11 668 Karr RPC plate, 10 779-780 Karstedt s catalyst, in silicone network preparation, 22 563 Karstenite, 5 785t Karyoplasts, 12 451, 458 Kashin-Beck disease, selenium and, 22 101 Kaspar s dynamic filter, 11 384 Katapinands, 24 44 Kauri-butanol value, 23 89 Kazakhstan... 

The titration process has been automated so that batches of samples can be titrated non-manually and the data processed and reported via printouts and screens. One such instrument is the Metrohm 670 titroprocessor. This incorporates a built-in control unit and sample changer so that up to nine samples can be automatically titrated. The 670 titroprocessor offers incremental titrations with variable or constant-volume steps (dynamic or monotonic titration). The measured value transfer in these titrations is either drift controlled (equilibrium titration) or effected after a fixed waiting time pK determinations and fixed end points (e.g. for specified standard procedures) are naturally included. End-point titrations can also be carried out. 

Various pH sensors have been built with a fluorescent pH indicator (fluorescein, eosin Y, pyranine, 4-methylumbelliferone, SNARF, carboxy-SNAFL) immobilized at the tip of an optical fiber. The response of a pH sensor corresponds to the titration curve of the indicator, which has a sigmoidal shape with an inflection point for pH = pK , but it should be emphasized that the effective pKa value can be strongly influenced by the physical and chemical properties of the matrix in which the indicator is entrapped (or of the surface on which it is immobilized) without forgetting the dependence on temperature and ionic strength. In solution, the dynamic range is restricted to approximately two pH units, whereas it can be significantly extended (up to four units) when the indicator is immobilized in a microhetero-geneous microenvironment (e.g. a sol-gel matrix). 

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) . 

This chapter deals with the fundamental aspects of redox reactions in non-aque-ous solutions. In Section 4.1, we discuss solvent effects on the potentials of various types of redox couples and on reaction mechanisms. Solvent effects on redox potentials are important in connection with the electrochemical studies of such basic problems as ion solvation and electronic properties of chemical species. We then consider solvent effects on reaction kinetics, paying attention to the role of dynamical solvent properties in electron transfer processes. In Section 4.2, we deal with the potential windows in various solvents, in order to show the advantages of non-aqueous solvents as media for redox reactions. In Section 4.3, we describe some examples of practical redox titrations in non-aqueous solvents. Because many of the redox reactions are realized as electrode reactions, the subjects covered in this chapter will also appear in Part II in connection with electrochemical measurements. 

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