Chemistry Reference
In-Depth Information
the osmolytes present with hydrated water (Timasheff 1998b, 2002a). The accuracy,
applicability, and validity of OSA have been thus questioned.
The controversy necessitated a more rigorous theoretical foundation than
Equation 11.1 for biomolecular processes in the presence of osmolytes. Parsegian,
Rand, and Rau (2000) have indeed provided this foundation based upon the Gibbs-
Duhem equation,
∞
o
∂
∆
G
c
c
r
1
3
−
=
∆
N
−
∆
N
(11.2)
21
23
∂
µ
1
Tp
,
where Δ
N
21
and Δ
N
23
are the number of water (species 1) and osmolytes (species 3)
bound to the dilute protein (species 2). This equation is identical in form to the one
that was derived under the assumptions that: (i) there are binding sites for the solvent
molecules on the surface of the protein molecule; and that (ii) water and osmolytes
competitively bind to each of the binding sites (Schellman 1987).
In contrast to the binding model approaches, Parsegian and coworkers have been
able to derive Equation 11.2 purely thermodynamically from the Gibbs-Duhem
equation. Furthermore, according to the main assumption of OSA, Δ
N
23
= 0, which
leads to -β∂Δ
r
G
o
/∂ ln
a
1
= Δ
N
21
. OSA has found a theoretical foundation in a solvent-
binding model and the Gibbs-Duhem equation (Parsegian, Rand, and Rau 2000).
The debate, however, went on further: Is Equation 11.2 valid? Does it describe
solvation accurately? Timasheff emphasized that Δ
N
21
and Δ
N
23
(although Timasheff
used a different notation) are purely phenomenological parameters representing
site
occupancy
, which have
no real physical meaning
(Timasheff 2002a, 2002b). He
has also argued that these parameters are indeterminates, because they are coupled
to conform to Equation 11.2, and that Equation 11.2 is the only relationship that
is known to connect them. Are these statements valid? It is FST that answers this
question, through which all the confusion regarding the foundation, interpretation,
and validity of OSA can be resolved (Shimizu 2004). The following represent FST's
answers to all the main theoretical points of the controversy.
QUESTION 1
Is there really any physical meaning to Δ
N
21
and Δ
N
23
?
Answer 1:
Yes (Shimizu 2004): (i) Equation 11.2 has been derived rigorously from FST (Chitra
and Smith 2001b; Shimizu 2004); and (ii) FST shows that
N
21
and
N
23
(for each of the
conformations) are defined microscopically through the solute-solvent and solute-
cosolvent radial distribution function
g
2i
(
r
),
∞
∫
[
]
()
−
2
N
=
4
π
c
gr
1
rdr
(11.3)
2
i
i
2
i
0
