Solvation function

First results from our fluorescence upconversion experiments are shown in Fig. 2, which displays the solvation-functions of C343 in bulk water and adsorbed on ZrC>2 nanoparticles. The response in bulk water confirms the previously reported results of bimodal dynamics [8] and a corresponding behaviour can be found for the dye bound to Z1O2, indicating that similar processes are involved. The results from biexponential fits to the solvation function S(t) of C343 in pure water and at the ZrCh-water interface are listed in Table 1. In both cases we find a fast decay time of about 100 fs and a slower decay of about 750 fs. We can see that the individual decay times stay similar and only the relative contributions change, resulting in an overall somewhat faster solvation for adsorbed dyes. 

According to the simple continuum model, the microscopic solvation function C(t) should decay exponentially with a time constant that is... 

The left-hand side of (15.26) is, by Eq. (15.23), a linear response approximation of the corresponding solvation energies difference. This makes it possible for us to write a linear response expression for the solvation function which is defined by... 

The nonequilibrium solvation function iS (Z), which is directly observable (e.g. by monitoring dynamic line shifts as in Fig. 15.2), is seen to be equal in the linear response approximation to the time correlation function, C(Z), of equilibrium fluctuations in the solvent response potential at the position of the solute ion. This provides a route for generalizing the continuum dielectric response theory of Section 15.2 and also a convenient numerical tool that we discuss further in the next section. 

Fig. 15.3 The nonequilibrium solvation function S(t) (full lines) and the solvation correlation functions C(i) for a model solute ion of diameter 3.1 A in acetonitrile computed with the positive solute (dotted line) and neutral solute (dashed line). (From M. Maroncelli, J. Chem. Phys. 94, 2084 (1991).)...

Figure 15.3 shows the results of computer simulations of solvation of a model ion in acetonitrile (CH3CN). The simulations produce the solvation function S t) for... 

Fig. 15.4 The experimental solvation function for water using sodium salt of coumarin-343 as a probe. The line marked expt. is the experimental solvation fimction S(t) obtained from the shift in the fluorescence spectrum. The line marked q is a simulation result based on the linear response ftinction C(t). The line Marked 5 is the linear response function for a neutral atomic solute with Lennard Jones parameters of the oxygen atom. (From R. Jimenez, G. R. Fleming, P. V. Kumar, and M. Maroncelli, Nature 369, 471 (1994).)...

Fig. 2 Solvation function of coumarin 343 dye in water and adsorbed on Zr02...

Figure 4.3.2. The linear response relaxation function C(t) (dashed and dotted lines] and the non-equilibrium solvation function S(t) (solid line) computed for the Stockmayer-CH3Cl model deseribed in Section 4. In the nonequilibrium simulation the ion charge is switehed on at t = 0. The dotted and dashed lines rq>re-sent C(t) obtained from equihbiium simulations with uneharged and charged i

Table 4.3.1. Relaxation times x obtained from fitting the short time component of the solvation function to the function S(t) =exp[-(t/x) ]. The fitting is done for S(t) > 0.3 [From Ref. 11a].

Figure 4.3.4. The solvation energy, (a) and the non-equilibrium solvation function S(t) (b), plotted against time (after switching the ion charge from 0 to e at t = 0) for different solvent models characterized by the parameter p (Eq. [4.3.35]). Dotted line, p = 0 solid line, p-0.019 dashed line, p =0.25 dashed-dotted line, p 8. [From Ref. 11a].

Figure 4.3.5.(a) The solvation energy E(t) and (b) the solvation function S(t) associated with the three solvation shells defined in the text, plotted against time after the ion charge is switched on, for the system with p-0.019. Solid line, nearest shell dotted line, second shell, dashed line, outer shell. [From Ref. 11a]. 

This deviation from linearity shows itself also in the solvation dynamics. Figure 4.3.7 shows the linear response functions and the non-equilibrium solvation function, C(t) and S(t), respectively, computed as before, for the di-ether H(CH20CH2)2CH3 solvent. Details of this simulations are given in Ref. 1 lb. If linear response was a valid approximation all the lines in Figure 4.3.7 The two lines for C(t) that correspond to q=0 and q=l, and the two lines for S(t) for the processes q=0—K =l and the process q=l—X =0, would coalesce. The marked differences between these lines shows that linear response theory fails forfliis system. 

Another way to consider protein hydration is to extend the concept of the solvent accessible surface (cf. O section Solvent-Accessible Surface ) applying continuum dielectrics models. For example, combination of the electrostatic and an appropriate hydrophobic potential, accounting for hydrophilic, and hydrophobic interactions, respectively, maybe used as a solvation function, which considerably increases the reliability of protein structure predictions (Lin et al. 2007). 

Lin, M. S., Fawzi, N. L., Head-Gordon, T. (2007). Hydrophobic potential of mean force as a solvation function for protein structure prediction. Structure, 15, 111,... 

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