Supplementary Material for
The Non-Uniform Early Structural Response of Globular Proteins to Cold Denaturing
Conditions: a Case Study with Yfh1
Prathit Chatterjee, Sayan Bagchi* and Neelanjana Sengupta*
Physical Chemistry Division, CSIR-National Chemical Laboratory, Pune 411008, India
________________________
To whom correspondence should be addressed.
Email: n.sengupta@ncl.res.in, s.bagchi@ncl.res.in.
1
Figure SI 1: IR absorption spectra for H1 at Ts (black) and Tc (blue).
2
Calculation of Tetrahedral Order Parameter
We have calculated the tetrahedral order parameter (Q)1,2 of water molecules (considering only
the water oxygen atoms as potential hydrogen bonding sites) within the hydration shell of the
protein as,
2
3 3 4 
1
Q 1   cos j k  
8 j 1 k j1
3
(1)
θjk represents the angle formed between the O-O vectors i,j and i,k from the oxygen atom (i)
with

its nearest
neighbors (j
and
k;
≤
4). The order parameter value of 1
resembles a perfect tetrahedral structure of water resembling its ice-state. The average values of
Q range from 0 to 1.Water molecules lying between the first and the second solvation shell of the
protein surface being maximally ordered,3 we have considered the water molecules which lie
within 2.5 and 4 Å of the protein heavy atoms (see Figure 3 b).
3
Figure SI 2: Distributions of the tetrahedral order parameter (Q) for bulk water, hydrophobic
beta sheet domain and hydrophobic alpha helical domain at a) Ts and b) Tc. Insets show the
expanded views for the range Q = 0.5 – 0.8. P(Q) denotes the probability of the corresponding Q
distributions, while P(Q)max corresponds to the maximum value of the corresponding probability.
4
Figure SI 3: Plots of radial distribution function (g(r)), and (∆g(r)) [or g(r)Tc - g(r)Ts)]; for Yfh1
and thermally stable Ubq. a) plots of g(r) of Ubq between backbone carbonyl carbon atoms of
the protein and water oxygen atoms at Ts (black) and Tc (blue), b) Plots of ∆g(r) of Ubq (black
straight line) and Yfh1 (black dashed line).
5
Figure SI 4: Plots of protein-water radial distribution function (g(r)) at, a) the BetaH domains of
Yfh1 at Ts (black) and Tc (blue); b) the BetaH domains of Ubq at Ts (black) and Tc (blue); c) the
HelixH domains of Yfh1 at Ts (black) and Tc (blue); and d) the HelixH domains of Ubq at Ts
(black) and Tc (blue).
6
Figure SI 5: Probability distributions of water densities near the surfaces of sidechains of a)
BetaH and b) HelixH, of thermally stable Ubq; at Ts (black), Tc (blue).
7
Figure SI 6: Comparison of the probability distributions of water densities near the surfaces of
sidechains of a) BetaH and b) HelixH of Yfh1; at Ts (black), Tc (blue) and Th (red).
8
Cumulative Configurational Entropy
We have calculated the configurational entropy for the backbone heavy atoms of the protein
Yfh1 as well as of its specific domains of interest for the whole trajectory at temperatures Tc, Ts
and Th by Schlitter’s method.4 The initial frame in each simulated trajectory has been used as the
respective reference, to remove the translational as well as the rotational motions with respect to
the center of mass of the systems. From the Schlitter’s method, the absolute entropy can be
approximately obtained as
1
 k Te 2 1
1
b
2
S abs S  k bln det1 
M M 2 
2
2



(2)
where kb being the Boltzmann’s constant, ħ the Planck’s constant divided by 2, e the Euler’s
number, M the the mass matrix of 3N dimension containing N atomic masses of the system and σ
is the covariance matrix. The elements in the covariance matrix can be denoted as

 ij  xi  xi  x j  x j

where, xi and xj are the Cartesian coordinates of the selected atoms.
9
(3)
Figure SI 7: Cumulative configurational entropy per atom of Yfh1 for the backbone heavy
atoms of a) the whole protein, b) the beta domains, and c) the betaH domains; at Ts (black), Tc
(blue) and Th (red).
10
Domains
SASAi
SASAc
% change
SASAs
(Tc)
% change
(Ts)
AllH
117.9
146.4
24.2
137.7
16.8
AllNH
147.5
159.9
8.4
145.6
-1.3
Beta
93.2
148.5
59.3
120.4
29.2
BetaH
135.6
201.3
48.4
163.9
20.9
BetaNH
153.3
197.7
29.0
169.3
10.4
Table SI 1: SASA/residues (of the side-chains) of Yfh1 for the hydrophobic (AllH) and nonhydrophobic domains (AllNH) of the whole protein, along with that of the hydrophobic (BetaH)
and non-hydrophobic (BetaNH) beta sheet domains, calculated for the initial snapshot (SASAi),
and for the last 50 ns of simulations at Tc (SASAc) and Ts (SASAs).
11
References
1
P. L. Chau and A. J. Hardwick, Mol. Phys. 93 (3), 511 (1998).
2
J. R. Errington and P.G. Debenedetti, Nature 409 (6818), 318 (2001).
3
N. Bhattacharjee and P. Biswas, Biophys. Chem. 158 (1), 73 (2011).
4
J.r. Schlitter, Chem. Phys. Lett. 215 (6), 617 (1993).
12