Chemistry Reference
In-Depth Information
fluctuations can also be extracted directly from light scattering data (Kirkwood and
Goldberg 1950; Blanco et al. 2011). Comparison of these types of data indicates that
one can observe sizeable differences in KBI values obtained using different activity
datasets (Perera et al. 2005), although the major differences are usually restricted
to the KBI values between species that are present at low concentrations. The dif-
ferences are also usually largest for systems that display far from ideal behavior. A
database of binary TCFIs and DCFIs for a wide variety of small molecule binaries
has been provided (Wooley and O'Connell 1991).
Computer simulations represent one of the most common approaches to deter-
mining the local fluctuations. However, there are some technical difficulties, which
can arise during the analysis of a typical simulation (see Chapter 6 for a full dis-
cussion). Most evaluations of the KBIs have used the integration approach, in con-
trast to the actual particle number fluctuations. Furthermore, as the vast majority of
simulations are performed for closed periodic systems, one is naturally limited to
performing the integration out to some cutoff distance from the particle of interest.
This seems reasonable given the similarities between the RDFs in open and closed
systems (Weerasinghe and Pettitt 1994). Hence, one can define distance-dependent
KBIs (and even distance-dependent thermodynamic functions) such that
R
∫
()
−
()
2
2
GR
()
≈
4
π
gr
1
rdr
(1.100)
ij
ij
0
where
R
is some distance at which the RDFs are essentially unity.
In favorable cases, the integral converges and one observes a limiting constant
value for the KBI (Weerasinghe and Smith 2003c; Bentenitis, Cox, and Smith 2009).
More typically, there can be significant statistical noise or artifacts that obscure the
real limiting behavior, depending on the system size used in the simulation (Perera
et al. 2006; Wedberg et al. 2010). Several studies have investigated this problem with
a variety of suggested solutions (see also Chapters 6 and 7). The effect of system size
on the KBI values has also been studied (Schnell et al. 2011). The problem seems to
be particularly acute when determining the isothermal compressibility. The situa-
tion appears to be significantly improved when examining the partial molar volumes
and chemical potential derivatives, presumably as these involve differences in the
KBIs (Nichols, Moore, and Wheeler 2009). However, this might not always be the
case as indicated in Chapter 6. Fortunately, the values of the resulting properties can
often be tested by other approaches—typically finite difference compressibilities or
partial molar volumes obtained from the simulated densities. However, checking the
chemical potential derivatives is quite time consuming.
Another issue arises when determining the KBIs or local distributions around
infinitely dilute solutes. In particular, special care must be taken when determin-
ing the solvent and cosolvent distributions around a single protein solute, proper-
ties that are required input for calculation of preferential binding described by
Equation 1.87. When using finite systems, it is sometimes necessary to adjust the
bulk distribution (
m
3
) during the analysis. For instance, the ratio of cosolvent to
solvent molecules in the bulk region is not equal to the ratio of total molecules
