Supporting Information for. DNA elasticity from short DNA to nucleosomal DNA

Transcription

1 Supporting Information for DNA elasticity from short DNA to nucleosomal DNA Ashok Garai, 1 Suman Saurabh, 1 Yves Lansac, 2 and Prabal K. Maiti* 1 1 Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore-12, India 2 GREMAN, Université François Rabelais, CNRS UMR 7347, 372 Tours, France (Dated: July 23, 2) This supporting information contains the following sections with figures: I. Distribution of Na + ions around the bare DNA II. RMSD of various FLSDs III. Variation of ln(p(θ)) as a function of 1 cos(θ) for various FLSDs IV. Calculation of persistence lengths for various TESDs V. Calculation of stretch modulus for various FLSDs and TESDs VI. Hydrogen bond analysis VII. Calculation of stretch modulus for TESDs using conformational energy analysis VIII. RMSD for NCP DNA IX. Calculation of persistence lengths for various SNDs X. Calculation of stretch modulus for NCP DNA XI. End-to-End length distribution XII. Comparison of bending rigidity of TESD with SND XIII. Comparison between AMBER and CHARMM force fields XIV. A note on the bending angle distribution XV. Various summary tables

2 2 Radial distribution Radial distribution Radial distribution 12 bp mm 1 2 mm 4 R (Å) R (Å) R (Å) 24 bp R (Å) R (Å) R (Å) 38 bp R (Å) R (Å) R (Å) 6 bp R (Å) R (Å) R (Å) FIG. S1: DNA-Na + radial distribution function as a function of time and radial distance R. Peaks in the distributions indicate significant DNA-Na + correlations, which become vanishingly small after 7Å. I. DISTRIBUTION OF Na + IONS AROUND THE BARE DNA We plot Na + distribution around various FLSD DNA in Fig. S1. We observe that peak of the radial distribution function does not change much, signifying that the simulation time is much larger than the time required for ions to attain a reasonable good distribution around the DNA. II. RMSD OF VARIOUS FLSDs Fig. S2 shows RMSD for ds-dna of different lengths at different salt concentrations. The values at which RMSDs saturate show little dependence on salt concentration. But they depend strongly on DNA length. As the DNA length increases, RMSD value increases, implying a larger deviation from the initial structure. This originates from a larger bending of DNA with increasing DNA length.

3 3 a b RMSD (Å) c d FIG. S2: RMSD plot for four different FLSD (a) 12bp, (b) 24bp, (c) 38bp, and (d) 6bp for various salt concentrations, (red), mm (blue) and 2mM (yellow)., III. VARIATION OF ln(p(θ)) AS A FUNCTION OF 1 cos(θ) FOR VARIOUS FLSDs Persistence length is obtained from the fitting of the bend-angle distribution using Eq.(2) of the main text. ln(p(θ)) as a function of 1 cos(θ) for various FLSds are shown in Fig. S3. IV. CALCULATION OF PERSISTENCE LENGTHS FOR VARIOUS TESDs Persistence length for TESDs was calculated using method similar to that used for FLSDs. Plot of ln(p(θ)) as a function of 1 cos(θ) for various TESDs are shown in Figs. S4, S. Fig S6 shows the variation of the persistence length with salt concentration for various ds-dna. V. CALCULATION OF STRETCH MODULUS FOR VARIOUS FLSDs AND TESDs Stretch modulus of various ds-dna was calculated by fitting the contour length distributions using a Gaussian function and then using Eq.() of the main text. Contour length distributions for various DNAs are shown in Figs. S7, S8. Stretch modulus as a function of salt concentrations for various TESDs is plotted and compared in Fig. S9.

4 4 lnp(θ) bp 6 bp mm mM cos(θ) mm 2mM FIG. S3: (color online) Plot of ln(p(θ)) as a function of 1 cos(θ) for 38 bp and 6 bp ds-dna FLSD at different salt concentrations. Discrete data points (color: red) are obtained from our MD simulations. Persistence lengths (l p) for respective ds-dna are calculated by fitting the slope with Eq. (2) (see main text) and is shown by straight line (color: blue). VI. HYDROGEN BOND ANALYSIS Hydrogen bond analysis for various DNAs are shown in Figs. S1, S11, S11, S13.

5 VII. CALCULATION OF STRETCH MODULUS FOR TESDS USING CONFORMATIONAL ENERGY ANALYSIS Variation of stretch modulus with salt concentrations for TESDs calculated using conformational energy analysis is shown in Fig. S14. VIII. RMSD FOR NCP DNA RMSD for NCP DNA with and without tails is shown in Fig. S. RMSD of NCP without tails is larger than that in presence of tails. The histone tails stabilize the binding of DNA to histone core. Removal of the tails causes unwinding of the DNA super helix at the termini giving rise to a larger RMSD. IX. CALCULATION OF PERSISTENCE LENGTHS FOR VARIOUS SNDs lnp(θ) as a function of 1 cos(θ) for SNDs with and without tails at different salt concentrations is shown in Fig. S16. Persistence length as a function of salt concentrations for SNDs with and without salt concentrations is shown in Fig. S17. X. CALCULATION OF STRETCH MODULUS FOR NCP DNA Contour length distribution for SND with and without tails with different salt concentrations is shown in Fig. S18. Stretch modulus calculated using different methods are plotted and compared in Figs. S19, S2, S2, S21, S22.

6 6 12 bp 24 bp lnp(θ) mm -.8 mm mM 2mM cos(θ) FIG. S4: (color online) Plot of ln(p(θ)) as a function of 1 cos(θ) for 12 bp and 24 bp TESD at different salt concentrations. Discrete data points (color: red) are obtained from our MD simulations. Persistence lengths (l p) for respective ds-dna are calculated by fitting the slope with Eq. (2) (see main text) and is shown by straight line (color: blue).

7 7 lnp(θ) bp 6 bp mm mM cos(θ) mm 2mM FIG. S: (color online) Plot of ln(p(θ)) as a function of 1 cos(θ) for 38 bp and 6 bp TESD at different salt concentrations. Discrete data points (color: red) are obtained from our MD simulations. Persistence lengths (l p) for respective ds-dna are calculated by fitting the slope with Eq. (2) and is shown by straight line (color: blue).

8 8 Persistence length (nm) bp 24 bp 38 bp 6 bp Salt concentration (mm) FIG. S6: Persistence length as a function of salt concentration for 12bp, 24bp, 38bp, 6bp TESD. P(L) bp 16 24bp mm 2mM mm 2mM L/L FIG. S7: Contour length distribution for 12 bp and 24bp TESD at different salt concentrations. Discrete data points are obtained from our MD simulations and the solid lines are obtained by fitting using Eq.() (see main text).

9 bp mm 2mM bp mm 2mM 1 1 P(L) bp mm 2mM L/L bp mm 2mM FIG. S8: Contour length distribution for 38bp and 6bp FLSD (left panel) and TESD (right panel) at different salt concentrations. Discrete data points are obtained from our MD simulations and the solid lines are obtained by fitting using Eq.() (see main text). γ G (pn) bp 24 bp 38 bp 6 bp Expt Salt concentrations (mm) FIG. S9: Stretch modulus (γ G) as a function of salt concentration for 12bp, 24bp, 38bp, 6bp TESD.

10 bp 24 bp Number of H-bonds mm mm FIG. S1: Number of hydrogen bonds as a function of time for 12 bp (first column) and 24 bp (second column) FLSD for different salt concentrations.

11 bp 6 bp Number of H-bonds mm mm FIG. S11: Number of hydrogen bonds as a function of time for 38 bp (first column) and 6 bp (second column) FLSD for different salt concentrations.

12 bp 24 bp Number of H-bonds mm mm FIG. S12: Number of hydrogen bonds as a function of time for 12 bp (first column) and 24 bp (second column) TESD for different salt concentrations.

13 13 Number of H-bonds 38 bp 6 bp mm mm FIG. S13: Number of hydrogen bonds as a function of time for 38 bp (first column) and 6 bp (second column) TESD for different salt concentrations.

14 14 γ cl (pn) bp 24 bp 38 bp 6 bp Salt concentrations (mm) FIG. S14: Stretch modulus (γ cl ) as a function of salt concentration for 12bp, 24bp, 38bp, 6bp TESD. RMSD (Å) a FIG. S: RMSD plots for FLND for the case (a) with tails (b) without tails at various salt concentrations, (red), mm (blue) and 2mM (green). b

15 NCP (with tails) NCP (no tail) mm mm lnp(θ) mM 2mM cos(θ) FIG. S16: (color online) ln(p(θ)) as a function of 1 cos(θ) for SND with and without tails at different salt concentrations. Discrete data points (color: red) are obtained from our MD simulations. Persistence lengths (l p) for respective ds-dna are calculated by fitting the slope with Eq. (2) (see main text) and is shown by straight line (color: blue).

16 16 Persistence length (nm) NCP-with tails NCP-without tail Salt concentration (mm) FIG. S17: Persistence length as a function of salt concentration for SND with and without tails. P(L) NCP (with tails) mm 2mM L/L NCP (no tail) mm 2mM FIG. S18: Contour length distribution for SND with and without tails with different salt concentrations. Discrete data points are obtained from our MD simulations and the solid lines are obtained by fitting with using Eq.() (see main text).

17 γ G (pn) γ WLC (pn) Salt concentrations (mm) 8 FIG. S19: (color online) Comparison between γ G (red) and γ WLC (blue) at different salt concentrations for FLND with and without tails. Filled data points and empty data points represent NCP with and without tails, respectively γ G (pn) γ WLC (pn) Salt concentrations (mm) 8 FIG. S2: Comparison between γ G (red) and γ WLC (blue) at different salt concentrations for SND with and without tails. Filled data points and empty data points represent NCP with and without tails, respectively. XI. END-TO-END LENGTH DISTRIBUTION End-to-end length distribution for various FLSD, FLND and TESD, SND at different salt concentrations is shown in Fig. S23.

18 γ cl (pn) γ etel (pn) Salt concentrations (mm) FIG. S21: (color online) Comparison between γ cl (red) and γ etel (blue) at different salt concentrations for FLND with and without tails. Filled data points and empty data points represent NCP with and without tails, respectively γ cl (pn) γ etel (pn) Salt concentrations (mm) FIG. S22: (color online) Comparison between γ cl (red) and γ etel (blue) at different salt concentrations for SND with and without tails. Filled data points and empty data points represent NCP with and without tails, respectively. XII. COMPARISON OF BENDING RIGIDITY OF TESD WITH SND Bending rigidity as a function of salt concentration for various TESD and SND is shown in Fig. S24. XIII. COMPARISON BETWEEN AMBER AND CHARMM FORCE FIELDS RMSD and End-to-end length distribution for 24 bp FLSD in absence of salt using two different force fields, AMBER and CHARMM, are shown in Fig. S2, and Fig. S26, respectively. Simulation with CHARMM force field shows a

19 19 P(R) bp.6.4 FLSD FLSD 24bp FLSD 38bp FLSD NCP (with tails) NCP FLND R 6bp FLND R/R TESD 24bp TESD 38bp NCP SND mm 2mM TESD TESD NCP (no tail) 12bp 6bp SND R/R FIG. S23: End-to-end length distribution for various FLSD, FLND (left panel) and TESD, SND (right panel) at different salt concentrations. Discrete data points are obtained from the MD simulations and the solid lines are the gaussian fits.

20 2 κ (pn-nm 2 ) bp 24bp 38bp 6bp NCP(with tails) NCP(no tail) Salt concentrations (mm) snd FIG. S24: Bending rigidity (κ) as a function of salt concentration for 12bp, 24bp, 38bp, 6bp TESD, SND with and without tails. smaller deviation from the initial B-DNA structure. XIV. A NOTE ON THE BENDING ANGLE DISTRIBUTION Small fluctuation in θ further reduces Eq.(3) (see main text) to the following equation: ( N lnp(θ) = ln )+ 12 [ L ln cos 1 (cos(θ)) ] (1 cos(θ))(1+cos(θ)) l p (1 cos(θ)) L (S1) Eq.(S1) indicates that a plot between lnp(θ) and (1 cos(θ)) gives a shape different from a descending straight line. We use Eq.(S1) to fit our data and extract the value of persistence length. Again the method of obtaining persistence length is different. Thus to identify the persistence length value from the other we name it as l g p. Note Eq.(3) (see main text) and Eq.(S1) are applicable to short and intermediate length of DNA. We report l p values obtained from different methods in tables (SI, SIII). XV. VARIOUS SUMMARY TABLES

21 21 RMSD [Å] AMBER CHARMM 1 2 Time [ns] FIG. S2: (color online) RMSD with respect to the minimized structure using two different force fields AMBER ff1 and CHARMM36 for 24 base pair double stranded DNA in condition. P(R) CHARMM 14 AMBER 12 FLSD CHARMM AMBER TESD R/R FIG. S26: End-to-end distance distribution for 24 bp FLSD (left) and TESD (right) using two different force fields AMBER ff1 and CHARMM 36.

22 22 TABLE SI: Elastic properties for FLSD and FLND System Salt L mp (nm) lp(nm) ls p (nm) lp g (nm) γ WLC(pN) γ G (pn) concn ± ± ± ± ± bp mm ± ± ±. 7± ± 2 2 mm ± ± ±.74 49±8 234 ± ± ± ±.44 7± 871 ± bp mm ± ± ± ± 7 ± 1 2 mm ± ± ±.4 412±12 17 ± ± ± ± ±28 98 ± 2 38 bp mm ± ± ± ± ± 1 2 mm ± ± ± ± ± ± ±.68.3 ±.82 12± ± 6 bp mm ± ± ± ± ± 17 2 mm ± ± ± 1 233± 828 ± ± ± ± ± ± 1 NCP mm ± ± ± ± ± 39 2 mm ± ± ± ± ± 328 NCP ± ± ± ± ± (no tail) mm ± ± ± ± ± 3 2 mm ± ± ± ± ± 218 TABLE SII: Elastic properties for FLSD and FLND System Salt γ cl (pn) γ etel (pn) κ (pn-nm 2 ) R mp Å γetel G concn ± , ±.84, 9.24 ±.7 12 bp mm ± , ± 2, 13.3 ±.81 2 mm ± , ±,3.77± ± ± bp mm ± ± mm ± ± ± ± bp mm ± ± mm ± ± ± ± bp mm ± ± mm ± ± ± ± 9.14 NCP mm ± ± mm ± ± 72.9 NCP ± ± 64.2 (no tail) mm ± ±.48 2 mm ± ± 33.27

23 23 TABLE SIII: Elastic properties for TESD and SND System Salt L mp (nm) lp(nm) ls p(nm) lp(nm) g γ WLC(pN) γ G (pn) concn ± ± ± ± 1924 ± bp mm ± ± ± 3 76 ± ± 39 2 mm ± ± ±6 82 ± ± ± ± ±.44 7 ± ± 24 bp mm ± ± 3.33 ± ± ± 13 2 mm ± ± ± ± ± ± ± ± ± ± 2 38 bp mm ± ± ± ± 981 ± 2 mm ± ± ± ± ± ± ± ± ± ± 2 6 bp mm ± ± ± 839 ± ± 27 2 mm ± ± ±. 243 ± ± ± ± ± ± ± 18 NCP mm ± ± ± ± ± mm ± ± ± ± ± 31 NCP ± ± ± ± ± 271 (no tail) mm ± ± ± ± ± mm ± ± ± ± ± 238 TABLE SIV: Elastic properties for TESD and SND System Salt γ cl (pn) γ etel (pn) κ (pn-nm 2 ) R mp Å concn ± ± bp mm ± ± mm ± ± ± ± bp mm ± ± mm ± ± ± ± bp mm ± ± mm ± ± ± ± bp mm ± ± mm ± ± ± ±31.2 1NCP mm ± ± mm ± ± 16.2 NCP ± ± (no tail) mm ± ± mm ± ± γ etel G TABLE SV: Elastic properties of the 24 bp TESD at condition Force field L mp (nm) R (nm) lp(nm) γwlc(pn) γg (pn) γ cl (pn) γ etel (pn) κ (pn-nm 2 ) R mp (nm) γ G etel (pn) CHARMM ± ± ± ± 1. AMBER ± ± ± ± 27.44

24 24 TABLE SVI: Details of regression analysis for the persistence length of various FLSDs and FLND System 1 cos(θ) (range selected for fitting) correlation coefficient (r) bp mm mm bp mm mm bp mm mm bp mm mm NCP mm (with tails) 2 mm NCP mm (without tail) 2 mm TABLE SVII: Details of regression analysis for the persistence length of various TESDs and SND System 1 cos(θ) (range selected for fitting) correlation coefficient (r) bp mm mm bp mm mm bp mm mm bp mm mm NCP mm (with tails) 2 mm NCP mm (without tail) 2 mm