Supplementary data for [Denaturation and Renaturation Behaviors of Short
DNA in a Confined Space]
Huaping Li,1,2 Zilu Wang,1,2 Ningning Li,3 Xuehao He2* and Haojun Liang3
1
Department of Polymer Science and Engineering, School of Chemical Engineering and Technology, Tianjin
University, Tianjin 300072, China
2
Department of Chemistry, School of Science, Tianjin University, and Collaborative Innovation Center of
Chemical Science and Engineering (Tianjin), Tianjin 300072, China
3
Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei
230026, China
1. WHAM procedure for treating configurations of PMF and PES
1.1
Potential of mean force (PMF)
We first calculate the pair ratio  and the energy E of each frame from the trajactory of REMD
simulation and figure out the maximum and minimum of the system energy, E_max and E_min,
respectively. Then we discretize the pair ratio and the energy into 16 bins j (0=0, 1=1/15, …, 15=1)
and 200 bins Ek (E0, E1, …, E199), respectively. Each set (j, k) represents a state in WHAM. Then the
probability of state (j, k) in the ith temperature Pi, (j, k) is related to the unbiased probability P(j, k)0 in the
transition temperature of Tmbulk via
pi,(j, k)  f ici,(j, k) p(j, k) 0 ,
where fi is chosen to make

j, k
(1)
pi,(j, k)  1 and ci, (j, k) is the temperature biasing factor estimated by
ci,(j, k)  exp[ (  i   0 ) Ek ] .
Then P(j, k)0 for each state is obtained by iterating the following two functions until the
convergence is reached.
 n

 N fc
16
p(j, k)
0
i 1 i, (j, k)
16
i 1
,
(2)
i i i, (j, k)
f i -1   j, k ci, (j, k) p(j, k) 0 ,
(3)
where ni, (j, k) is the amount of the state (j, k) in the ith temperature and Ni is the total amount of
configurations in it. Initial fi for each temperature is set as 0.0001.
Finally, we sum P(j, k)0 from the 200 bins of energy for each j to get P(j)0. PMF is estimated by
Fj  kBTm bulk ln p( j)0 ,
1
(4)
1.2
Potential energy surface (PES)
In the calculation of PES, j in the Pi, (j, k) of the PMF is replaced by a set of two-dimensional
parameters (dB1-B’15, dB15-B’1). dB1-B’15 and dB15-B’1 are the distances between the end bases of two
ssDNA strands. B and B’ indicate bases from the sense and antisense strands respectively and the
number marks the base index in the strand. Other operations in WHAM procedure are same with
those of PMF.
2
2. Supplementary Figures
This section provides the melting curves (Figure S1), the specific heat curves (Figure S2), the PMF
(Figure S4) and the PES (Figure S5 and S6) of Seq2, Seq3 and Seq4, along with figures (Figure S3, S7
and S8) to assist discussion in the main paper.
Figure S1. Melting curves of Seq2, Seq3 and Seq4 under cylindrical (cyl) and spherical (sph) confinements.
The melting temperature, Tm, increases as Rc (the confinement radius) reduces and the melting curve declines
remarkably for all the systems.
3
Figure S2. Specific heat curves of Seq2, Seq3 and Seq4 under cylindrical (cyl) and spherical (sph)
confinements. As Rc decreases, Tm increases and the phase transition becomes weak and broad for all the
systems.
4
Figure S3. Differences of the melting temperatures obtained from the Specific heat curves and the melting
curves of the four sequences under the criterion of φ* = 0.5 (a) and φ* = 0.4 (b). Under the latter criterion,
most points are within the range of -4 to 4 K with merely four exceptions, showing a better concordance than
φ* = 0.5. Rc-1 to Rc-4 correspond to (4.5, 3.15, 1.8, 1.44 nm) for cylindrical (cyl) and (5.4, 4.5, 3.6, 2.7 nm) for
spherical (sph) confinements, respectively.
5
Figure S4. Free energy profiles of Seq2, Seq3 and Seq4 under cylindrical (cyl) and spherical (sph)
confinements. The corresponding melting temperatures Tmbulk are 318.3 K (Seq2), 315.1 K (Seq3) and 348.5 K
(Seq4). For clarity, all the curves are shifted to match the minimum points of the native state. The relative free
energy of ssDNA increases as the confinement becomes strong, indicating that the renaturation process is
promoted by the confinement.
6
Figure S5. Potential energy surface (PES) of different sequences (1: Seq2, 2: Seq3, 3: Seq4) under cylindrical
confinements (a: 1.44 nm, b: 1.8 nm, c: 3.15 nm, d: 4.5 nm, e: bulk). Arrows point to the representative
snapshots of the region on the PES. Short blue arrows close to configurations indicate the directions of strands.
Under strong confinement, short ssDNA is hard to rotate in the cylinder, resulting in ‘X’ or ‘band’ shape PES.
In contrast, weak confinement causes more expanded PES. In picture 3b, the asymmetrical PES along the
diagonal line is resulted from the specific sequence of Seq4 and the typical conformation is also shown.
7
Figure S6. Potential energy surface (PES) of different sequences (1: Seq2, 2: Seq3, 3: Seq4) under spherical
confinements (a: 2.7 nm, b: 3.6 nm, c: 4.5 nm, d: 5.4 nm). The PES of the bulk systems refer to the
corresponding PES in Figure S5. As the confinement becomes strong, the relative areas of the native and the
denatured states increase simultaneously on the PES, making the phase transition weaker and much easier.
8
Figure S7. Distribution of the length (a) and radius (b) of ssDNA and dsDNA in the melting temperature in
bulk. ssDNA shows a broader distribution than dsDNA without the pairing limit. But their maximum
probabilities locate at almost the same point. Consequently, it is a tenable assumption that ssDNA and dsDNA
can be viewed as the same rigid rod in the proposed theoretical model in the main paper. It should be noted
that it is a specific character for short DNA strands. The characters of long ssDNA and dsDNA are obviously
different.
9
Figure S8. Plotting of (a) ln(–lnfrod) against ln(Rc) and (b) the negative derivative –d(ln(–lnfrod))/d(ln(Rc))
against Rc, with different radius and length parameters for ssDNA and dsDNA obtained from the peak value in
Figure S7. Compared with Figure 11 in the main paper, the changes of the plots due to the slight changes of
parameters are negligible. The meanings of the lines and symbols in the plot are identical to Figure 11.
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3. Supplementary Tables
TABLE S1. Melting temperatures of DNA obtained from the melting curves under different confinements and
in bulk, according to the criterion of φ* = 0.5. It is obviously shown that Tm increases as the confinement size
decreases.
1.44
1.8
cylinder 3.15
4.5
Seq1
357.9±2.1
340.4±5.0
329.6±3.2
323.7±2.0
Tm( =0.5) (K)
Seq2
Seq3
358.2±2.5
350.8±4.6
341.0±4.2
337.5±2.0
327.0±1.0
324.0±1.8
323.3±3.0
318.7±2.2
Seq4
389.4±2.0
372.5±2.8
357.5±2.4
352.4±1.4
2.7
3.6
4.5
5.4
341.0±1.9
334.3±1.3
327.4±2.2
324.1±2.3
337.9±0.8
330.7±2.4
324.4±1.7
323.8±1.9
329.2±2.4
326.1±3.2
318.2±1.8
317.1±2.4
373.3±1.8
367.6±2.2
356.1±1.6
353.0±3.2
315.6±1.8
314.1±5.8
311.7±4.6
343.7±3.9
*
Radius (nm)
sphere
Bulk
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TABLE S2. Criteria φ* on the melting curves corresponding to the Tm on the specific heat curves. Obviously,
choosing the criterion of φ* = 0.4 makes Tm from the melting curves and the specific heat curves match better.
Radius (nm)
φ*
1.44
1.8
cylinder 3.15
4.5
Seq1
0.42
0.38
0.39
0.4
Seq2
0.41
0.4
0.43
0.4
Seq3
0.47
0.39
0.43
0.43
Seq4
0.33
0.36
0.38
0.4
2.7
3.6
4.5
5.4
0.39
0.4
0.4
0.41
0.44
0.43
0.42
0.42
0.42
0.44
0.42
0.43
0.34
0.37
0.38
0.38
0.41
0.41
0.42
0.4
sphere
Bulk
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