- {
- “cells”: [
- {
“cell_type”: “markdown”, “metadata”: {
“raw_mimetype”: “text/restructuredtext”
}, “source”: [
“How to calculate Global Elasticity?n”, “===================================n”, “n”, “To calculate global elasticity,
dnaMD globalElasticitycommand can be used. However, it takes HDF5 file as input.n”, “Following steps can be performed to generate HDF5 files. The tutorial file can be downloaded here. We will prepare HDF5n”, “file for both free and bound DNA.n”, “n”, “Calculate stretching twisting and bending motionsn”, “————————————————-n”, “n”, “Both free and bound DNA is superimposed on to the same DNA structure. Careful that bending calculation is fitting dependent.n”, “Therefore, at first we aligned both free and bound DNA to a common DNA structure as follows”]
}, {
“cell_type”: “code”, “execution_count”: null, “metadata”: {}, “outputs”: [], “source”: [
“%%bashn”, “n”, “# Align bound DNAn”, “echo 6 0 | gmx trjconv -f inputs/F1_complex_DNA.xtc -s inputs/dna.tpr -n inputs/dna.ndx -o complex_dna_aligned.xtc -fit rot+transn”, “n”, “# Align free DNAn”, “echo 6 0 | gmx trjconv -f inputs/F1_free_DNA.xtc -s inputs/dna.tpr -n inputs/dna.ndx -o free_dna_aligned.xtc -fit rot+trans”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“1. Run do_x3dna on DNA trajectory,
-nofitis used because DNA is already superimposed to a common DNA structure using trjconv.”]
}, {
“cell_type”: “code”, “execution_count”: null, “metadata”: {
“raw_mimetype”: “text/restructuredtext”
}, “outputs”: [], “source”: [
“%%bashn”, “n”, “# For free DNAn”, “echo 2 | do_x3dna -f free_dna_aligned.xtc -s inputs/dna.tpr -n inputs/dna.ndx -ref -noavg -nofit -name freen”, “mv *_free.dat outputs/.n”, “n”, “# For bound DNAn”, “echo 2 | do_x3dna -f complex_dna_aligned.xtc -s inputs/dna.tpr -n inputs/dna.ndx -ref -noavg -nofit -name boundn”, “mv *_bound.dat outputs/.”
]
}, {
“cell_type”: “markdown”, “metadata”: {
“raw_mimetype”: “text/restructuredtext”
}, “source”: [
“2. Run dnaMD to extract the parameters from do_x3dna output files and save as HDF5 file. Also calculate global axis,n”, “curvature and tangents.”
]
}, {
“cell_type”: “code”, “execution_count”: 8, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“n”, “Loading parameters: [‘shift’, ‘slide’, ‘rise’, ‘tilt’, ‘roll’, ‘twist’]n”, “Reading file : L-BPS_free.datn”, “Reading frame 5000n”, “Finished reading…. Total number of frame read = 5001n”, “n”, “Loading parameters: [‘x-disp’, ‘y-disp’, ‘h-rise’, ‘inclination’, ‘tip’, ‘h-twist’]n”, “Reading file : L-BPH_free.datn”, “Reading frame 5000n”, “Finished reading…. Total number of frame read = 5001n”, “n”, “Loading parameters: [‘helical x-axis’, ‘helical y-axis’, ‘helical z-axis’]n”, “Reading file : HelAxis_free.datn”, “Reading frame 5000n”, “Finished reading…. Total number of frame read = 5001n”, “Fitting spline curve on helical axis of frame 5000 out of 5001 framesn”, “Finished spline curve fitting…n”, ” … Calculating curvature and tangents n”, ” … Finishedn”, “n”, “Loading parameters: [‘shift’, ‘slide’, ‘rise’, ‘tilt’, ‘roll’, ‘twist’]n”, “Reading file : L-BPS_bound.datn”, “Reading frame 10000n”, “Finished reading…. Total number of frame read = 12001n”, “n”, “Loading parameters: [‘x-disp’, ‘y-disp’, ‘h-rise’, ‘inclination’, ‘tip’, ‘h-twist’]n”, “Reading file : L-BPH_bound.datn”, “Reading frame 10000n”, “Finished reading…. Total number of frame read = 12001n”, “n”, “Loading parameters: [‘helical x-axis’, ‘helical y-axis’, ‘helical z-axis’]n”, “Reading file : HelAxis_bound.datn”, “Reading frame 10000n”, “Finished reading…. Total number of frame read = 12001n”, “Fitting spline curve on helical axis of frame 12000 out of 12001 framesn”, “Finished spline curve fitting…n”, ” … Calculating curvature and tangents n”, ” … Finishedn”
]
}
], “source”: [
“%%bashn”, “n”, “# For free DNAn”, “dnaMD saveAsH5 -tbp 27 -i outputs/L-BPS_free.dat,outputs/L-BPH_free.dat,outputs/HelAxis_free.dat -o free_dna.h5n”, “dnaMD axisCurv -tbp 27 -bs 2 -be 25 -ctan -scp 100 -s 1000 -cta 30 -io free_dna.h5 -ap free_dna_axis.pdbn”, “n”, “# For bound DNAn”, “dnaMD saveAsH5 -tbp 27 -i outputs/L-BPS_bound.dat,outputs/L-BPH_bound.dat,outputs/HelAxis_bound.dat -o bound_dna.h5n”, “dnaMD axisCurv -tbp 27 -bs 2 -be 25 -ctan -scp 100 -s 1000 -cta 30 -io bound_dna.h5 -ap bound_dna_axis.pdb”
]
}, {
“cell_type”: “markdown”, “metadata”: {
“raw_mimetype”: “text/restructuredtext”
}, “source”: [
“Now, we have HDF5 files of both free and bounds DNA. It can be used for the calculation of elastic properties. These filesn”, “can be used with either [dnaMD Python module](http://do-x3dna.readthedocs.io/en/latest/notebooks/calculate_elasticity_tutorial.html) or
dnaMD globalElasticity.n”, “n”, “n”, “Bending Stretching Twist Modulusn”, “——————————–n”, “n”, “Following command calculate Bending Stretching Twist modulus matrix. Output matrix will be stored in csv file.n”, “Elastic modulus matrix is printed as output and average values of contour length and cumulative twist anglen”, “is also printed.”]
}, {
“cell_type”: “code”, “execution_count”: 1, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“=========== Elastic Modulus Matrix ===========n”, “n”, ” 337.233 28.506 -6.984 -20.710n”, ” 28.506 373.863 7.977 39.509n”, ” -6.984 7.977 1080.722 -96.198n”, ” -20.710 39.509 -96.198 448.349n”, “n”, “=========== ====================== ===========n”, “n”, “========================= Average Values ==========================n”, “n”, “Bending-1 Angle Bending-2 Angle Contour Length Sum. Twist n”, ” 0.021 0.068 5.358 9.543 n”, “n”, “=========== ====================== ====================== ===========n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD globalElasticity -i free_dna.h5 -tbp 27 -bs 4 -be 20 -estype BST -paxis X -o elastic_modulus_BST.csv”
]
}, {
“cell_type”: “markdown”, “metadata”: {
“raw_mimetype”: “text/restructuredtext”
}, “source”: [
“The above modulus matrix is in this form:n”, “n”, “$$\text{modulus matrix} =n”, “\begin{bmatrix}n”, “M_{Bx} & M_{Bx,By} & M_{Bx,S} & M_{Bx,T} \\n”, “M_{Bx,By} & M_{By} & M_{By,S} & M_{By,T} \\n”, “M_{Bx,S} & M_{By,S} & M_{S} & M_{S,T} \\n”, “M_{Bx,T} & M_{Bx,T} & M_{S,T} & M_{T}n”, “\end{bmatrix}n”, “$$n”, “n”, “Where:n”, “n”, “* $M_{Bx}$ - Bending-1 stiffness in one planen”, “* $M_{By}$ - Bending-2 stiffness in another orthogonal planen”, “* $M_{S}$ - Stretch Modulusn”, “* $M_{T}$ - Twist rigidityn”, “* $M_{Bx,By}$ - Bending-1 and Bending-2 couplingn”, “* $M_{By,S}$ - Bending-2 and stretching couplingn”, “* $M_{S,T}$ - Stretching Twsiting couplingn”, “* $M_{Bx,S}$ - Bending-1 Stretching couplingn”, “* $M_{By,T}$ - Bending-2 Twisting couplingn”, “* $M_{Bx,T}$ - Bending-1 Twisting couplingn”, “n”, “n”, “Stretching Twist Modulusn”, “————————n”, “n”, “Following command calculate Bending Stretching Twist modulus matrix. Output matrix will be stored in csv file.n”, “Elastic modulus matrix is printed as output and average values of contour length and cumulative twist anglen”, “is also printed.”
]
}, {
“cell_type”: “code”, “execution_count”: 2, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“=========== Elastic Modulus Matrix ===========n”, “n”, “1080.380 -97.578n”, “-97.578 442.494n”, “n”, “=========== ====================== ===========n”, “n”, “========================= Average Values ==========================n”, “n”, “Contour Length Sum. Twist n”, ” 5.358 9.543 n”, “n”, “=========== ====================== ====================== ===========n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD globalElasticity -i free_dna.h5 -tbp 27 -bs 4 -be 20 -estype ST -o elastic_modulus_ST.csv”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“The above modulus matrix is in this form:n”, “n”, “$$\text{modulus matrix} =n”, “\begin{bmatrix}n”, “M_{S} & M_{S,T} \\n”, “M_{S,T} & M_{T}n”, “\end{bmatrix}n”, “$$n”, “n”, “Where:n”, “n”, “* $M_{S}$ - Stretch Modulusn”, “* $M_{T}$ - Twist rigidityn”, “* $M_{S,T}$ - Stretching Twsiting couplingn”, “n”, “Convergence in Modulusn”, “———————-n”, “n”, “Same command can be used to calculate elasticity as a function of time with option n”, “
-ot/--output-timeand save it in csv format file. This result can beused to checkn”, “their convergence. n”, “n”, “* If this option is used,-fgap/--frame-gapis an essential option.n”, “* This options also gives final value and error as the output on display.n”, “* The output file is in csv format and can be opened as spreadsheet.n”, “n”, “NOTE: Elastic properties cannot be calculated using a single frame because n”, “fluctuations are required. Therefore, here time means trajectory between zero n”, “time to given time.”]
}, {
“cell_type”: “code”, “execution_count”: 3, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“==============================================n”, “Elasticity Value Errorn”, “———————————————-n”, “bend-1 337.233 3.932n”, “bend-2 373.863 4.935n”, “stretch 1080.722 24.015n”, “twist 448.349 29.356n”, “bend-1-bend-2 28.506 4.685n”, “bend-2-stretch 7.977 7.251n”, “stretch-twist -96.198 13.450n”, “bend-1-stretch -6.984 7.131n”, “bend-2-twist 39.509 35.576n”, “bend-1-twist -20.710 5.081n”, “==============================================n”, “n”, “=====================================n”, “Elastic modulus as a function of timen”, “=====================================n”, “#Time, bend-1, bend-2, stretch, twist, bend-1-bend-2, bend-2-stretch, stretch-twist, bend-1-stretch, bend-2-twist, bend-1-twistn”, “1000.000, 584.19567, 363.51886, 1121.88830, 1506.57584, 41.49043, -101.57973, 112.06246, -254.22188, -74.92882, 252.68516n”, “2000.000, 354.70978, 367.93829, 1032.49032, 662.58414, -18.43006, -53.55808, 9.82719, -81.25370, -207.81222, 111.70108n”, “3000.000, 380.26015, 359.63694, 967.63012, 543.68667, 5.70038, -76.61296, -8.92719, -88.41420, -95.81366, 56.24528n”, “.n”, “.n”, “.n”, “118000.000, 335.33614, 371.13759, 1082.41850, 449.84105, 27.64596, 10.92246, -97.17016, -7.92023, 36.92839, -17.34603n”, “119000.000, 335.79993, 373.00012, 1081.59948, 449.85747, 28.30290, 9.58966, -96.91853, -6.18165, 37.45497, -19.36140n”, “120000.000, 337.23300, 373.86276, 1080.72201, 448.34909, 28.50566, 7.97658, -96.19760, -6.98413, 39.50860, -20.71008n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD globalElasticity -i free_dna.h5 -tbp 27 -bs 4 -be 20 -estype BST -paxis X -fgap 100 -em block -ot modulus_time_BST.csvn”, “n”, “# Print first and last 3 line of output filen”, “echo "====================================="n”, “echo "Elastic modulus as a function of time"n”, “echo "====================================="n”, “head -4 modulus_time_BST.csvn”, “printf ".\n.\n.\n"n”, “tail -3 modulus_time_BST.csv”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“Some of the plots from above data can be found [here](http://do-x3dna.readthedocs.io/en/latest/notebooks/calculate_elasticity_tutorial.html#Convergence-in-bending,-stretching-and-twisting-with-their-couplings)n”, “n”, “***n”, “n”, “Same as above but only for stretching and twisting motions.”
]
}, {
“cell_type”: “code”, “execution_count”: 4, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“==============================================n”, “Elasticity Value Errorn”, “———————————————-n”, “stretch 1080.380 22.847n”, “twist 442.494 19.169n”, “stretch-twist -97.578 14.389n”, “==============================================n”, “n”, “=====================================n”, “Elastic modulus as a function of timen”, “=====================================n”, “#Time, stretch, twist, stretch-twistn”, “1000.000, 991.91168, 1373.35825, 200.50841n”, “2000.000, 1004.78021, 516.21083, 3.60912n”, “3000.000, 931.30826, 509.38341, -16.08887n”, “.n”, “.n”, “.n”, “118000.000, 1081.86818, 444.95480, -98.78361n”, “119000.000, 1081.20986, 444.61885, -98.34127n”, “120000.000, 1080.37979, 442.49438, -97.57808n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD globalElasticity -i free_dna.h5 -tbp 27 -bs 4 -be 20 -estype ST -paxis X -fgap 100 -gt "gmx analyze" -em "block" -ot modulus_time_ST.csvn”, “n”, “# Print first and last 3 line of output filen”, “echo "====================================="n”, “echo "Elastic modulus as a function of time"n”, “echo "====================================="n”, “head -4 modulus_time_ST.csvn”, “printf ".\n.\n.\n"n”, “tail -3 modulus_time_ST.csv”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“Global deformation free energyn”, “——————————n”, “n”, “To caluclate global deformation enrgy,
dnaMD globalEnergycan be used. At first, elastic matrix from referencen”, “DNA (most often free or unbound DNA) is calculated and subsequently this matrix is used to calculate deformation freen”, “energy of probe DNA (most often bound DNA).n”, “n”, “The deformation free energy is calculated using elastic matrix as followsn”, “n”, “$$G = \frac{1}{2L_0}\mathbf{xKx^T}$$n”, “n”, “$$\mathbf{x} = \begin{bmatrix}n”, ” (\theta^{x} - \theta^{x}_0) & (\theta^{y} - \theta^{y}_0) & (L - L_0) & (\phi - \phi_0)n”, ” \end{bmatrix}$$n”, “n”, “Where, $\mathbf{K}$, $\theta^{x}_0$, $\theta^{y}_0$, $L_0$ and $\phi_0$ is calculated from reference DNA while $\theta^{x}$, $\theta^{y}$, $L$ and $\phi$ is calculated for probe DNA from each frame.n”, “n”, “This command gives output energy as a function of time in csv file and also average energies with error.”]
}, {
“cell_type”: “code”, “execution_count”: 5, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“==============================================n”, “Energy(kJ/mol) Average Errorn”, “———————————————-n”, “full 27.714 0.724n”, “diag 27.012 0.751n”, “stretch 2.468 0.157n”, “twist 15.061 0.478n”, “st_coupling -0.743 0.040n”, “b1 1.477 0.180n”, “b2 8.005 0.266n”, “bend 9.718 0.386n”, “bs_coupling 0.034 0.002n”, “bt_coupling 0.825 0.020n”, “bb_coupling 0.235 0.020n”, “st 26.269 0.713n”, “bs 11.984 0.499n”, “bt 25.369 0.634n”, “==============================================n”, “n”, “===========================================================n”, “Deformation free energy of bound DNA as a function of timen”, “===========================================================n”, “#Time, full, diag, stretch, twist, st_coupling, b1, b2, bend, bs_coupling, bt_coupling, bb_coupling, st, bs, btn”, “0.000, 29.76525, 29.12752, 3.05586, 16.01787, -0.96687, 0.27243, 9.78136, 10.18484, 0.05805, 1.09664, 0.13105, 28.16064, 13.16770, 27.16829n”, “10.000, 27.69000, 26.82145, 1.78113, 13.65491, -0.68154, 3.00373, 8.38168, 11.78823, 0.02173, 0.69127, 0.40282, 26.13991, 13.18827, 25.73159n”, “20.000, 32.65326, 31.73848, 3.36328, 15.22752, -0.98900, 0.93046, 12.21722, 13.41835, 0.05997, 1.11574, 0.27067, 30.74949, 16.57094, 29.49094n”, “.n”, “.n”, “.n”, “49980.000, 28.48093, 28.59762, 4.40662, 16.38502, -1.17429, 0.45068, 7.35530, 7.95214, 0.05514, 0.91465, 0.14616, 27.42332, 12.26774, 25.10564n”, “49990.000, 33.18350, 32.91519, 3.56658, 21.03477, -1.19700, 0.05849, 8.25534, 8.36962, 0.06281, 1.21256, 0.05579, 31.71819, 11.94323, 30.56117n”, “50000.000, 30.81292, 29.94787, 1.86541, 19.01796, -0.82313, 0.67654, 8.38796, 9.25575, 0.03664, 1.02777, 0.19124, 29.12474, 10.96655, 29.11023n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD globalEnergy -ir free_dna.h5 -ip bound_dna.h5 -tbp 27 -bs 4 -be 20 -estype BST -et "all" -paxis X -gt "gmx analyze" -em "block" -o energy_all_BST.csvn”, “n”, “# Print first and last 3 line of output filen”, “echo "==========================================================="n”, “echo "Deformation free energy of bound DNA as a function of time"n”, “echo "==========================================================="n”, “head -4 energy_all_BST.csvn”, “printf ".\n.\n.\n"n”, “tail -3 energy_all_BST.csv”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“Some of the plots from above data can be found [here](http://do-x3dna.readthedocs.io/en/latest/notebooks/calculate_elasticity_tutorial.html#Deformation-free-energy-of-bound-DNA)n”, “n”, “**n”, “n”, “Deformation free energy can be calculated as the following terms:n”, “n”, “
full: Use entire elastic matrix – all motions with their couplingn”, “*diag: Use diagonal of elastic matrix – all motions but no couplingn”, “*b1: Only bending-1 motionn”, “*b2: Only bending-2 motionn”, “*stretch: Only stretching motionn”, “*twist: Only Twisting motionsn”, “*st_coupling: Only stretch-twist coupling motionn”, “*bs_coupling: Only Bending and stretching couplingn”, “*bt_coupling: Only Bending and Twisting couplingn”, “*bb_coupling: Only bending-1 and bending-2 couplingn”, “*bend: Both bending motions with their couplingn”, “*st: Stretching and twisting motions with their couplingn”, “*bs: Bending (b1, b2) and stretching motions with their couplingn”, “*bt: Bending (b1, b2) and twisting motions with their couplingn”, “n”, “Whenallis used, all above terms were calculated.”]
}, {
“cell_type”: “code”, “execution_count”: 6, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“==============================================n”, “Energy(kJ/mol) Average Errorn”, “———————————————-n”, “full 15.398 0.353n”, “diag 17.211 0.408n”, “stretch 2.581 0.137n”, “twist 14.630 0.362n”, “st_coupling -0.906 0.037n”, “==============================================n”, “n”, “===========================================================n”, “Deformation free energy of bound DNA as a function of timen”, “===========================================================n”, “#Time, full, diag, stretch, twist, st_couplingn”, “0.000, 24.65120, 27.93891, 4.01772, 23.92119, -1.64386n”, “10.000, 16.45031, 18.42131, 2.11880, 16.30251, -0.98550n”, “20.000, 22.50793, 25.46474, 3.54666, 21.91808, -1.47841n”, “.n”, “.n”, “.n”, “49980.000, 13.37563, 15.94228, 5.74292, 10.19936, -1.28332n”, “49990.000, 17.67070, 20.02852, 2.88301, 17.14551, -1.17891n”, “50000.000, 16.73218, 18.89026, 2.53138, 16.35888, -1.07904n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD globalEnergy -ir free_dna.h5 -ip bound_dna.h5 -tbp 27 -bs 4 -be 24 -estype ST -et "all" -gt "gmx analyze" -em "block" -o energy_all_ST.csvn”, “n”, “# Print first and last 3 line of output filen”, “echo "==========================================================="n”, “echo "Deformation free energy of bound DNA as a function of time"n”, “echo "==========================================================="n”, “head -4 energy_all_ST.csvn”, “printf ".\n.\n.\n"n”, “tail -3 energy_all_ST.csv”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“Same as above but only for stretching and twisting motions.n”, “n”, “Local elastic propertiesn”, “————————n”, “n”, “Local elastic properties can be caluclated using either local base-step parameters or local helical base-step parameters.n”, “n”, “In case of base-step parameters: Shift ($Dx$), Slide ($Dy$), Rise ($Dz$), Tilt ($\tau$), Roll ($\rho$) and Twist ($\omega$), following elastic matrix is calculated.n”, “n”, “$$n”, “\mathbf{K}_{base-step} = \begin{bmatrix}n”, “K_{Dx} & K_{Dx,Dy} & K_{Dx,Dz} & K_{Dx,\tau} & K_{Dx,\rho} & K_{Dx,\omega} \\n”, “K_{Dx,Dy} & K_{Dy} & K_{Dy,Dz} & K_{Dy,\tau} & K_{Dy,\rho} & K_{Dy,\omega} \\n”, “K_{Dx,Dz} & K_{Dy,Dz} & K_{Dz} & K_{Dz,\tau} & K_{Dz,\rho} & K_{Dz,\omega} \\n”, “K_{Dx,\tau} & K_{Dy,\tau} & K_{Dz,\tau} & K_{\tau} & K_{\tau, \rho} & K_{\tau,\omega} \\n”, “K_{Dx,\rho} & K_{Dy,\rho} & K_{Dz,\rho} & K_{\tau, \rho} & K_{\rho} & K_{\rho,\omega} \\n”, “K_{Dx,\omega} & K_{Dy,\omega} & K_{Dz,\omega} & K_{\tau, \omega} & K_{\rho, \omega} & K_{\omega} \\n”, “\end{bmatrix}n”, “$$n”, “n”, “In case of helical-base-step parameters: x-displacement ($dx$), y-displacement ($dy$), h-rise ($h$), inclination ($\eta$), tip ($\theta$) and twist ($\Omega$), following elastic matrix is calculated.n”, “n”, “$$n”, “\mathbf{K}_{helical-base-step} = \begin{bmatrix}n”, “K_{dx} & K_{dx,dy} & K_{dx,h} & K_{dx,\eta} & K_{dx,\theta} & K_{dx,\Omega} \\n”, “K_{dx,dy} & K_{dy} & K_{dy,h} & K_{dy,\eta} & K_{dy,\theta} & K_{dy,\Omega} \\n”, “K_{dx,h} & K_{dy,h} & K_{h} & K_{h,\eta} & K_{h,\theta} & K_{h,\Omega} \\n”, “K_{dx,\eta} & K_{dy,\eta} & K_{h,\eta} & K_{\eta} & K_{\eta, \theta} & K_{\eta,\Omega} \\n”, “K_{dx,\theta} & K_{dy,\theta} & K_{h,\theta} & K_{\eta, \theta} & K_{\theta} & K_{\theta,\Omega} \\n”, “K_{dx,\Omega} & K_{dy,\Omega} & K_{h,\Omega} & K_{\eta, \Omega} & K_{\theta, \Omega} & K_{\Omega} \\n”, “\end{bmatrix}n”, “$$”
]
}, {
“cell_type”: “code”, “execution_count”: 7, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“=========== ============== Elastic Matrix =============== ===========n”, “n”, ” 150.32688 -12.74081 -4.99484 -0.86502 -0.08939 -0.16720n”, ” -12.74081 129.99578 30.42056 0.27454 -0.58620 -2.06912n”, ” -4.99484 30.42056 504.89222 0.65083 -0.06531 0.21751n”, ” -0.86502 0.27454 0.65083 0.03433 -0.00104 0.00052n”, ” -0.08939 -0.58620 -0.06531 -0.00104 0.01295 0.01427n”, ” -0.16720 -2.06912 0.21751 0.00052 0.01427 0.05907n”, “n”, “=========== ====================== ====================== ===========n”, “n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD localElasticity -i free_dna.h5 -tbp 27 -bs 4 -be 7 -o local_elasticity_4-7bps.csv”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“Local elastic properties as a function of timen”, “———————————————-n”, “n”, “Same command can be used to calculate elasticity as a function of time with option n”, “
-ot/--output-timeand save it in csv format file. This result can be used to checkn”, “their convergence. n”, “n”, “* If this option is used,-fgap/--frame-gapis an essential option.n”, “* The output file is in csv format and can be opened as spreadsheet.n”, “n”, “NOTE: Elastic properties cannot be calculated using a single frame because n”, “fluctuations are required. Therefore, here time means trajectory between zero n”, “time to given time.”]
}, {
“cell_type”: “code”, “execution_count”: 8, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“=====================================n”, “Elastic matrix as a function of timen”, “=====================================n”, “#Time, shift, slide, rise, tilt, roll, twist, … … …n”, “2000.000, 158.96347, 127.71194, 503.26390, 0.03143, 0.01542, 0.05937, … … …n”, “4000.000, 150.93805, 126.16929, 467.98254, 0.03050, 0.01409, 0.06100, … … …n”, “6000.000, 147.43936, 132.39932, 480.47463, 0.03256, 0.01358, 0.06143, … … …n”, “.n”, “.n”, “.n”, “116000.000, 151.11253, 129.64049, 504.93262, 0.03417, 0.01293, 0.05897, … … …n”, “118000.000, 150.77496, 129.62910, 504.85789, 0.03426, 0.01296, 0.05910, … … …n”, “120000.000, 150.32688, 129.99578, 504.89222, 0.03433, 0.01295, 0.05907, … … …n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD localElasticity -i free_dna.h5 -tbp 27 -bs 4 -be 7 -fgap 200 -ot local_elasticity_time_4-7bps.csvn”, “n”, “# Print first 3 and last 3 line of first seven columns from output filen”, “echo "====================================="n”, “echo "Elastic matrix as a function of time"n”, “echo "====================================="n”, “head -4 local_elasticity_time_4-8bps.csv | awk ‘{print $1, $2, $3, $4, $5, $6 ,$7, "… … …"}’n”, “printf ".\n.\n.\n"n”, “tail -3 local_elasticity_time_4-8bps.csv | awk ‘{print $1, $2, $3, $4, $5, $6 ,$7, "… … …"}’”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“Local elastic properties of the consecutive overlapped DNA segmentsn”, “——————————————————————–n”, “n”, “Above method gives local elasticities of a small local segment of the DNA. However, we mostly interestedn”, “in large segment of the DNA. This large segment can be further divided into smaller local segments. n”, “For these smaller segments local elasticities can be calculated. Here these segments overlapped with each other.n”, “n”, “Same command can be used to calculate elasticity as a function of time with option n”, “
-os/--output-segmentsand save it in csv format file.n”, “n”, “* If this option is used,-fgap/--frame-gapis an essential option.n”, “* The output file is in csv format and can be opened as spreadsheet.n”]
}, {
“cell_type”: “code”, “execution_count”: 9, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“========================================n”, “Elasticity as a function of DNA segmentsn”, “========================================n”, “#bps, shift, shift-error, slide, slide-error, rise, rise-error, … … …n”, “4-7, 150.32688, 0.25654, 129.99578, 0.27262, 504.89222, 1.61893, … … …n”, “5-8, 162.67911, 0.46671, 122.65855, 0.47513, 510.18741, 1.36958, … … …n”, “6-9, 172.50587, 2.36981, 119.84961, 1.46698, 510.68380, 2.57983, … … …n”, “.n”, “.n”, “.n”, “15-18, 153.98831, 2.02295, 137.21947, 0.29044, 546.15664, 1.31991, … … …n”, “16-19, 188.51349, 1.91188, 148.97261, 0.46969, 521.74643, 1.14698, … … …n”, “17-20, 174.28796, 2.07481, 134.04039, 0.67123, 573.20011, 2.54414, … … …n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD localElasticity -i free_dna.h5 -tbp 27 -bs 4 -be 20 -span 4 -fgap 200 -gt "gmx analyze" -em "acf" -os local_elasticity_segments.csvn”, “n”, “# Print first 3 and last 3 line of first seven columns from output filen”, “echo "========================================"n”, “echo "Elasticity as a function of DNA segments"n”, “echo "========================================"n”, “head -4 local_elasticity_segments.csv | awk ‘{print $1, $2, $3, $4, $5, $6 ,$7, "… … …"}’n”, “printf ".\n.\n.\n"n”, “tail -3 local_elasticity_segments.csv | awk ‘{print $1, $2, $3, $4, $5, $6 ,$7, "… … …"}’”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“Local deformation energy of a local small segmentn”, “————————————————-n”, “At first, elastic matrix from reference DNA (most often free or unbound DNA) is calculated n”, “and subsequently this matrix is used to calculate deformation free energy of probe DNA n”, “(most often bound DNA).n”, “n”, “$$G = \frac{1}{2}\mathbf{xKx^T}$$n”, “n”, “When
helical='False'n”, “n”, “$$\mathbf{K} = \mathbf{K}_{base-step}$$n”, “n”, “$$\mathbf{x} = \begin{bmatrix}n”, ” (Dx_{i}-Dx_0) & (Dy_i - Dy_0) & (Dz_i - Dz_0) & (\tau_i - \tau_0) &n”, ” (\rho_i - \rho_0) & (\omega_i - \omega_0)n”, ” \end{bmatrix}$$n”, “n”, “n”, “Whenhelical='True'n”, “n”, “$$\mathbf{K} = \mathbf{K}_{helical-base-step}$$n”, “n”, “$$\mathbf{x} = \begin{bmatrix}n”, ” (dx_{i}-dx_0) & (dy_i - dy_0) & (h_i - h_0) & (\eta_i - \eta_0) &n”, ” (\theta_i - \theta_0) & (\Omega_i - \Omega_0)n”, ” \end{bmatrix}$$n”]
}, {
“cell_type”: “code”, “execution_count”: 10, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“==============================================n”, “Energy(kJ/mol) Average Errorn”, “———————————————-n”, “full 19.143 0.671n”, “diag 43.865 1.839n”, “shift 1.366 0.064n”, “slide 15.994 1.069n”, “rise 1.194 0.030n”, “tilt 1.705 0.040n”, “roll 6.365 0.365n”, “twist 17.242 0.781n”, “==============================================n”, “n”, “===============================================n”, “Local deformation energy as a function of timen”, “===============================================n”, “#Time, full, diag, shift, slide, rise, tilt, roll, twistn”, “0.000, 32.99568, 97.62372, 0.85609, 43.00855, 0.55182, 0.05174, 8.64099, 44.51453n”, “10.000, 24.91292, 63.21362, 0.18680, 31.85144, 0.31550, 2.74114, 5.80446, 22.31428n”, “20.000, 34.19821, 78.73263, 0.77440, 31.54860, 4.31769, 0.19352, 8.74777, 33.15064n”, “.n”, “.n”, “.n”, “49980.000, 17.43224, 50.92180, 0.07917, 12.95852, 2.46789, 0.92035, 5.74851, 28.74736n”, “49990.000, 18.86625, 58.72850, 3.25713, 25.11722, 0.01483, 1.27080, 1.81182, 27.25671n”, “50000.000, 19.01918, 49.56285, 2.16952, 13.54590, 1.86029, 4.52988, 4.38336, 23.07391n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD localEnergy -ir free_dna.h5 -ip bound_dna.h5 -tbp 27 -bs 10 -be 13 -et all -gt "gmx analyze" -em "block" -o local_energy_time_4-7bps.csvn”, “n”, “# Print first 3 and last 3 line from output filen”, “echo "==============================================="n”, “echo "Local deformation energy as a function of time"n”, “echo "==============================================="n”, “head -4 local_energy_time_4-7bps.csvn”, “printf ".\n.\n.\n"n”, “tail -3 local_energy_time_4-7bps.csv”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“Some of the plots from above data can be found n”, “[here](http://do-x3dna.readthedocs.io/en/latest/notebooks/calculate_elasticity_tutorial.html#Local-deformation-energy-of-a-local-small-segment)n”, “n”, “***n”, “n”, “Same as the above but energy is calculated using helical base-step parameters”
]
}, {
“cell_type”: “code”, “execution_count”: 11, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“==============================================n”, “Energy(kJ/mol) Average Errorn”, “———————————————-n”, “full 18.541 0.607n”, “diag 82.103 3.204n”, “x-disp 38.632 1.974n”, “y-disp 0.940 0.024n”, “h-rise 6.768 0.333n”, “inclination 15.242 0.857n”, “tip 1.288 0.030n”, “h-twist 19.232 0.825n”, “==============================================n”, “n”, “======================================================n”, “Local helical deformation energy as a function of timen”, “======================================================n”, “#Time, full, diag, shift, slide, rise, tilt, roll, twistn”, “0.000, 32.99568, 97.62372, 0.85609, 43.00855, 0.55182, 0.05174, 8.64099, 44.51453n”, “10.000, 24.91292, 63.21362, 0.18680, 31.85144, 0.31550, 2.74114, 5.80446, 22.31428n”, “20.000, 34.19821, 78.73263, 0.77440, 31.54860, 4.31769, 0.19352, 8.74777, 33.15064n”, “.n”, “.n”, “.n”, “49980.000, 17.43224, 50.92180, 0.07917, 12.95852, 2.46789, 0.92035, 5.74851, 28.74736n”, “49990.000, 18.86625, 58.72850, 3.25713, 25.11722, 0.01483, 1.27080, 1.81182, 27.25671n”, “50000.000, 19.01918, 49.56285, 2.16952, 13.54590, 1.86029, 4.52988, 4.38336, 23.07391n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD localEnergy -ir free_dna.h5 -ip bound_dna.h5 -tbp 27 -bs 10 -be 13 -et all -helical -gt "gmx analyze" -em "block" -o local_helical_energy_time_4-7bps.csvn”, “n”, “# Print first 3 and last 3 line from output filen”, “echo "======================================================"n”, “echo "Local helical deformation energy as a function of time"n”, “echo "======================================================"n”, “head -4 local_energy_time_4-7bps.csvn”, “printf ".\n.\n.\n"n”, “tail -3 local_energy_time_4-7bps.csv”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“Deformation energy of the consecutive overlapped DNA segmentsn”, “————————————————————-n”, “n”, “Above method gives energy of a small local segment of the DNA. n”, “However, we mostly interested in large segment of the DNA. This large segment n”, “can be further divided into smaller local segments. For these smaller segments n”, “local deformation energy can be calculated. Here these segments overlapped with each other.”
]
}, {
“cell_type”: “code”, “execution_count”: 12, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“==================================================n”, “Local deformation energy as a function of segmentsn”, “==================================================n”, “#bps, full, full-error, diag, diag-error, shift, shift-error, slide, slide-error, rise, rise-error, tilt, tilt-error, roll, roll-error, twist, twist-errorn”, “4-7, 10.44541, 0.15599, 16.11461, 0.50862, 0.95000, 0.02392, 8.97490, 0.44581, 1.17289, 0.13403, 1.71030, 0.05021, 1.08986, 0.03874, 2.21666, 0.17392n”, “5-8, 9.49626, 0.25053, 19.32846, 0.70809, 1.14060, 0.02737, 9.59726, 0.51038, 1.21808, 0.18759, 1.75363, 0.04521, 1.11454, 0.05955, 4.50435, 0.19880n”, “6-9, 10.52567, 0.28519, 20.09691, 0.54228, 1.22326, 0.02970, 11.45709, 0.43514, 1.51242, 0.08500, 1.90555, 0.04658, 1.31208, 0.11407, 2.68650, 0.09203n”, “.n”, “.n”, “.n”, “15-18, 13.98537, 0.52298, 41.05547, 2.63829, 1.04577, 0.02497, 17.01431, 0.86024, 2.44413, 0.14371, 1.78045, 0.04873, 1.78854, 0.20280, 16.98227, 2.09869n”, “16-19, 14.04847, 0.37844, 39.34525, 1.49491, 1.97148, 0.09511, 14.20378, 0.94662, 2.52573, 0.08194, 1.70940, 0.04099, 0.98835, 0.09072, 17.94652, 1.15043n”, “17-20, 7.89839, 0.32320, 14.91991, 0.78938, 1.03028, 0.02583, 5.81921, 0.49549, 1.40673, 0.06566, 1.46641, 0.03364, 1.05240, 0.14133, 4.14489, 0.38861n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD localEnergy -ir free_dna.h5 -ip bound_dna.h5 -tbp 27 -bs 4 -be 20 -span 4 -et all -gt "gmx analyze" -em "block" -os local_energy_segments.csvn”, “n”, “# Print first 3 and last 3 line from output filen”, “echo "=================================================="n”, “echo "Local deformation energy as a function of segments"n”, “echo "=================================================="n”, “head -4 local_energy_segments.csvn”, “printf ".\n.\n.\n"n”, “tail -3 local_energy_segments.csv”
]
}, {
“cell_type”: “markdown”, “metadata”: {}, “source”: [
“Some of the plots from above data can be found n”, “[here](http://do-x3dna.readthedocs.io/en/latest/notebooks/calculate_elasticity_tutorial.html#Deformation-energy-of-the-consecutive-overlapped-DNA-segments)n”, “n”, “***n”, “n”, “n”, “Same as the above but energy is calculated using helical base-step parameters”
]
}, {
“cell_type”: “code”, “execution_count”: 13, “metadata”: {}, “outputs”: [
- {
“name”: “stdout”, “output_type”: “stream”, “text”: [
“==========================================================n”, “Local helical deformation energy as a function of segmentsn”, “==========================================================n”, “#bps, full, full-error, diag, diag-error, x-disp, x-disp-error, y-disp, y-disp-error, h-rise, h-rise-error, inclination, inclination-error, tip, tip-error, h-twist, h-twist-errorn”, “4-7, 9.94039, 0.17649, 17.73868, 0.51652, 9.00892, 0.37199, 1.19946, 0.04468, 1.54174, 0.13701, 1.69527, 0.06446, 1.73424, 0.04823, 2.55906, 0.16107n”, “5-8, 9.01980, 0.22539, 19.49642, 0.57573, 8.19696, 0.26473, 1.36335, 0.06127, 1.48339, 0.27526, 1.60444, 0.08879, 1.76889, 0.04544, 5.07939, 0.32815n”, “6-9, 10.30985, 0.26888, 17.00383, 0.38032, 7.38157, 0.25950, 1.96202, 0.28106, 0.99682, 0.02458, 1.68845, 0.14166, 1.89859, 0.04606, 3.07639, 0.16278n”, “.n”, “.n”, “.n”, “15-18, 13.74199, 0.55739, 53.29447, 4.60218, 27.45388, 1.71961, 0.66820, 0.01620, 1.17571, 0.02924, 3.37921, 0.40760, 1.29946, 0.03306, 19.31802, 2.43431n”, “16-19, 12.60741, 0.33640, 46.34514, 2.01539, 19.89670, 0.90439, 0.90573, 0.04403, 1.01976, 0.02504, 1.68335, 0.09711, 1.12857, 0.06776, 21.71103, 1.22043n”, “17-20, 7.54442, 0.33087, 15.27288, 0.76005, 5.60088, 0.40791, 0.91852, 0.02377, 1.13807, 0.02707, 1.66290, 0.20744, 1.25180, 0.02884, 4.70071, 0.43934n”
]
}
], “source”: [
“%%bashn”, “n”, “dnaMD localEnergy -ir free_dna.h5 -ip bound_dna.h5 -tbp 27 -bs 4 -be 20 -span 4 -et all -helical -gt "gmx analyze" -em "block" -os local_helical_energy_segments.csvn”, “n”, “# Print first 3 and last 3 line from output filen”, “echo "=========================================================="n”, “echo "Local helical deformation energy as a function of segments"n”, “echo "=========================================================="n”, “head -4 local_helical_energy_segments.csvn”, “printf ".\n.\n.\n"n”, “tail -3 local_helical_energy_segments.csv”
]
}
], “metadata”: {
- “kernelspec”: {
“display_name”: “Python 3”, “language”: “python”, “name”: “python3”
}, “language_info”: {
- “codemirror_mode”: {
“name”: “ipython”, “version”: 3
}, “file_extension”: “.py”, “mimetype”: “text/x-python”, “name”: “python”, “nbconvert_exporter”: “python”, “pygments_lexer”: “ipython3”, “version”: “3.6.6”
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}