Supplementary Material
Velocity Autocorrelation Function (VACF):
The velocity autocorrelation function (VACF) is defined as


vi (t ).vi (0)
CV (t )  

vi (0).vi (0)
(1)

where vi (t ) is the velocity vector of the i-th atom (O or H) of a water molecule at time t. The
angular brackets denote averaging over all the atoms of a particular water type at different
reference initial times. The VACFs are separately calculated for the oxygen ( CVO (t ) ) and the
hydrogen ( CVH (t ) ) atoms of different types of water molecules around the complex and the free
forms of the protein and the carbohydrate, as shown in Fig. 1S. For comparison, the data for pure
FIG. 1S. Velocity autocorrelation function for the (a) oxygen ( CVO (t ) ) and (b) hydrogen
H
( CV
(t ) ) atoms of different types of water molecules around the protein and the carbohydrate
in the complexed and free forms. The water types and the drawing scheme used to represent
them are same as that described in Fig. 1(a) of the article. The results for water in pure bulk
state are also shown for comparison.
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bulk water are also included in the figure. The relaxation of CVO (t ) for pure bulk water is
characterized by an initial small bump followed by a dip. This is the so-called ‘caging effect’ that
arises from back-scattering of water oxygens due to their collisions with neighboring molecules.
The calculation reveals that compared to pure bulk water, the function CVO (t ) exhibits deeper
minima for water around the protein and the carbohydrate. Such enhanced caging effect is more
pronounced for water around the binding residues and in the common region of the complex.
This correlates well with increasingly restricted motions of the corresponding water molecules as
discussed in the article. Fig. 1S (b) shows that the function CVH (t ) for water hydrogen atoms
present in different regions around the complex and the free forms exhibits almost identical
behavior among themselves, which is similar to that observed for pure bulk water. CVH (t )
essentially characterizes the librational motions (hindered rotations) of water, and the general
oscillatory nature of the function with a significantly deeper minimum indicates stronger caging
effects on water librations. It is clear that water librations around the complex are not much
affected.
We further explored the effect of BW hydrogen bond formation on water VACFs for only
those water molecules that are bound by BW hydrogen bonds. The results are compared with that
of the free forms of the two molecules as well as with that for pure bulk water, as shown in Fig.
2S. It can be seen that the decay curves not only exhibit deeper minima compared to pure bulk
water, but those are more pronounced than that noticed when all the water molecules present in
the first hydration layers were considered (see Fig. 1S). It indicates increasing caging effects for
the bound water molecules, a direct consequence of strong BW hydrogen bonds and their slower
relaxations. Again, the effect is more for water molecules present in the common region and in
regions surrounding the binding residues. By comparing the results shown in Fig. 2S(b) with that
in Fig. 1S(b), we find that the function CVH (t ) for the bound water molecules exhibits relatively
more pronounced oscillations. This is consistent with enhanced caging effects for the bound
water molecules as compared to the other nearby water molecules.
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FIG. 2S. Velocity autocorrelation function for the (a) oxygen ( CVO (t ) ) and (b) hydrogen
H
( CV
(t ) ) atoms of different types of water molecules that are involved in BW hydrogen
bonds around the protein and the carbohydrate in the complexed and free forms. The water
types and the drawing scheme used to represent them are same as that described in Fig. 1(a)
of the article. The results for water in pure bulk state are also shown for comparison.
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