Thermodynamic stability, channels

Roux, B. Nina, M. Pomes, R. Smith, J., Thermodynamic stability of water molecules in the Bacteriorhodopsin proton channel a molecular dynamics and free energy perturbation study, Biophys. J. 1996, 71, 670-681... 

As seen above (equation (5)), the basis of the simple bioaccumulation models is that the metal forms a complex with a carrier or channel protein at the surface of the biological membrane prior to internalisation. In the case of trace metals, it is extremely difficult to determine thermodynamic stability or kinetic rate constants for the adsorption, since for living cells it is nearly impossible to experimentally isolate adsorption to the membrane internalisation sites (equation (3)) from the other processes occurring simultaneously (e.g. mass transport complexation adsorption to other nonspecific sites, Seen, (equation (31)) internalisation). 

The competition of homolytic cleavages is governed by Stevenson s rule (Chap. 6.2.2). Thermodynamic stability of the pairs of products formed is decisive in selecting the preferred fragmentation channel. 

However, details of this process including the mode of urea binding, the protonation state of individual surround protein residues, and the exact identity of the nucleophile are still under debate. Cyanate also was proposed as a possible intermediate in the urease mechanism (33). Recent quantum chemical calculations and molecular dynamics simulations indicated that hydrolytic and ehmination mechanisms might indeed compete, and that both are viable reaction channels for urease (34—37). Finally, an important issue is Why does urease require nickel as the metal of choice, whereas most other metallohydrolases use zinc While it was speculated that, inter alia, the relatively rigid and stable coordination environment around the Ni(II) ions as opposed to the higher kinetic lability and lower thermodynamic stability of Zn(II) complexes might play a role (31), this fundamental question has not yet been answered. 

The real occurrence of polymerization inside the channels was demonstrated in several ways. It does not occur, at least for a number of monomers, when there is a simple mixture of host and monomer without the formation of a clathrate or when the monomer is placed in the presence of solid substances unable to form inclusion compounds. Even in cases when polymerization does take place the structure of the polymer formed outside the channels differs from that obtained in proper conditions. The reaction rate is very temperature and pressure dependent and has a sheirp drop-off point beyond which reaction ceases. The boundaur y conditions for polymerization correspond to those which delimit the field of thermodynamic stability of the monomeric clathrate, determined by vapor pressure measurements or by DSC. This coincidence enables us to state that the two phenomena, monomer inclusion and polymerization, are strictly related. In addition, in some typical cases a structural change from monomer to polymer was directly observed inside the channels by X-ray analysis. 

The tryptophan synthase bienzyme complex from enteric bacteria provides an important example wherein RSSF has been used to good advantage for the study of both enzyme mechanism and protein structure-function relationships. This enzyme complex is composed of heterologous a- and P2-subunits arranged in a nearly linear a-(3-(l-a array (81). The a-subunit catalyzes the aldolytic cleavage of IGP to indole and G3P, while the P-subunit catalyzes the PLP-dependent condensation of i-Ser and indole to yield i-Trp. The aP-reaction is essentially the sum of the individual a- and P-reactions (scheme I). Indole, the common intermediate produced at the a-site, is direcdy channeled to the P-active site via a tunnel located in the interior of the protein complex which directly interconnects the a- and P-catalytic centers (81-84). Although the individual subunits may be isolated and are functional, formation of the bienzyme complex not only increases the catalytic activities of the separate subunits by nearly 100-fold, but also alters the thermodynamic stability of P-site reaction intermediates and introduces heterotropic allosteric interactions between sites. 

Figure 11 Hill plots are dose-response curves that describe the dependence of activity on monomer concentration. Hill analysis can differentiate between (a) unstable supramolecular active structures (n > 1 known stoichiometry, undetectable suprastructure) and (b) stable supramolecular or unimolecular active structures (n < 1 unknown stoichiometry, detectable suprastructure). Single channel lifetimes (t) differentiate between labile and inert active structures, whereas both open probabilities and Hill coefficients indicate thermodynamic stabilities.

To predict the chemical composition of a catalyst under the realistic conditions, one has to consider the stability of different extra-framework iron complexes at a finite temperature and also to take into account the presence of H O and during the catalyst preactivation. This information can be obtained via a statistical thermodynamic analysis based on the energetics predicted by DPT calculations. In the case of Fe/ZSM-5 zeolite, the following equilibrium reaction was considered to evaluate the thermodynamic stability of different species inside the zeolite channels ... 

In order to probe further the thermodynamic stability, the dissociation energies (D ) for various fragmentation channels of the clusters are considered. 

The Hill coefficient n obtained from the curve fit of the Cm profile of Class I channels and pores (Fig. 11.7a) corresponds to the number of monomers in the active supramolecule (if self-assembly indeed occurs from an excess monomer in solution. With self-assembly from excess dimer, the number of monomers per active supramolecule is 2n, and so on). The compatibility with the Hill equation further demonstrates the presence of excess monomer besides a small population of active supramolecule. The presence of excess monomer, in turn, reveals that the self-assembly of the channel or pore is an endergonic process. Structural studies of unstable n > 1 supramolecules at concentrations near the EC o by conventional methods are therefore meaningless. For example, NMR or IR measurements will report on the inactive monomers, whereas the unstable active structure of Class I channels and pores is invisible (see Section 11.4 for methods to selectively detect and study minority populations of active supramolecules). In BLMs, the thermodynamic instability of Class I channels and pores is expressed in low open probabilities Po (Fig. 11.4). The n > 1 of Class I channels and pores is unrelated to the kinetic stability expressed in short lifetimes for labile Class lA and long lifetimes for inert Class IB supramolecules. 

Cations are also important for the self-assembly of nueleotides. Wong and Wu have found that the eation-induced stability of a 5 -GMP structure is determined by the affinity of monovalent cations for the channel site (with the order > NH4" > Rb" > Na > Cs > Li" ). Polycations such as spermine also interact with quadruplex structures/ but their effects on the thermodynamics of the quadruplex are still not completely understood. 

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