Nucleic Acid Quadratic Indices of the “Macromolecular Graph’s Nucleotides Adjacency Matrix”. Modeling of Footprints after the Interaction of Paromomycin with the HIV-1 Ψ-RNA Packaging Region
Abstract
:Introduction
Materials and methods
Computational Methods
Purine and pyrimidine bases (RNA/ADN) | f1 | f2 | Є260/1000 | ΔE1 | ΔE2 |
---|---|---|---|---|---|
Adenine (A) | 0.28 | 0.54 | 15.4 | 4.75 | 5.99 |
Guanine (G) | 0.20 | 0.27 | 11.7 | 4.49 | 5.03 |
Uracil (U) | 0.18 | 0.3 | 9.9 | 4.81 | 6.11 |
Thymine (T) | 0.18 | 0.37 | 9.2 | 4.67 | 5.94 |
Cytosine (C) | 0.13 | 0.72 | 7.5 | 4.61 | 6.26 |
= 0 otherwise
Secondary structure of an RNA fragment of the SL 2 motif (see Figure 1) | Macromolecular graph’s: an undirected graph with multiple edges Gm | Xm = [G A C U G G U G A G U A C]; Xm ∈ℜ13 In the definition of
Xm, as macromolecular vector, the symbol of the bases is used to indicate the corresponding AND-RNA bases property, for instance, f1. That is: if we write A it means f1(A), adenine first oscillator strength values or some bases property, which characterizes each nucleotide in the nucleic acid molecule. So, if we use the canonical bases of ℜ13, the coordinates of any macromolecular vector Xm coincide with the components of that macromolecular vector. [Xm]t = [0.20 0.28 0.13 0.18 0.20 0.20 0.18 0.20 0.28 0.20 0.18 0.28 0.13] [Xm]t: Transposed of [Xm] and it means the vector of the coordinates of Xm in Canonical base of ℜ13 (a row matrix) [Xm]: vector of the coordinates of Xm in Canonical base of ℜ13 (a columns matrix) M1(Gm): Macromolecular graph’s nucleotide Adjacency Matrix | |||
= [mX]tM0(Gm) [mX] = 0.5662 | |||||
= [mX]tM1(Gm) [mX] = 1.7124 | |||||
= [mX]tM2(Gm) [mX] = 6.7533 | |||||
= [mX]tM3(Gm) [mX] = 25.3806 | |||||
= [mX]tM4(Gm) [mX] = 105.5649 | |||||
Nucleotide (N) | q0L(Xm, N) | q1L(Xm, N) | q2L(Xm, N) | q3L(Xm, N) | q4L(Xm, N) |
G285 | 0.04 | 0.134 | 0.666 | 2.154 | 9.654 |
A286 | 0.0784 | 0.1932 | 1.0668 | 3.5112 | 17.2256 |
C287 | 0.0169 | 0.1378 | 0.5369 | 2.8223 | 10.1634 |
U288 | 0.0324 | 0.1602 | 0.5328 | 2.0844 | 8.9226 |
G289 | 0.04 | 0.076 | 0.254 | 0.748 | 2.738 |
G290 | 0.04 | 0.076 | 0.156 | 0.422 | 1.136 |
U291 | 0.0324 | 0.072 | 0.1512 | 0.3492 | 1.0872 |
G292 | 0.04 | 0.092 | 0.232 | 0.786 | 2.8 |
A293 | 0.0784 | 0.2128 | 0.8652 | 3.3768 | 12.6308 |
G294 | 0.04 | 0.17 | 0.996 | 3.604 | 18.342 |
U295 | 0.0324 | 0.1872 | 0.4572 | 2.6136 | 8.6328 |
A296 | 0.0784 | 0.0868 | 0.5376 | 1.3608 | 7.4004 |
C297 | 0.0169 | 0.1144 | 0.3016 | 1.5483 | 4.8321 |
ARN fragment | 0.5662 | 1.7124 | 6.7533 | 25.3806 | 105.5649 |
= 1/2 kaij if vi or vj are contained within FR
= 0 otherwise
Footprinting Data
TOMOCOMD-CANAR Software
Statistical Analysis
Results and Discussion
Development of the Discrimination Function: Local (Nucleotide) quadratic indices and the probability of footprinting after RNA-Paromomycin interaction.
N = 101 λ = 0.43 D2 = 6.0 F(3.97) = 43.342 ρ = 10.1 p < 0.000
Local (Nucleotide) quadratic indices and modeling of Paromomycin’s affinity constant with HIV-1 Ψ-RNA
Nucleotide | ΔP%a | P%-cvb | Nucleotide | ΔP%a | P%-cvb | Nucleotide | ΔP%a | P%-cvb |
---|---|---|---|---|---|---|---|---|
Training Set (Nucleotide non-‘footprinted’) | ||||||||
RNA-A235 | 98.44 | 99.22 | RNA-A301 | 98.40 | 99.15 | RNA-A332 | 99.61 | 99.80 |
RNA-G241 | 90.65 | 94.94 | RNA-A302 | 99.41 | 99.70 | RNA-G333 | 86.70 | 92.78 |
RNA-C243 | -97.92* | 99.49* | RNA-U303 | 86.59 | 92.63 | RNA-A334 | 99.62 | 98.81 |
RNA-U244 | -92.03* | 97.05* | RNA-U304 | 89.23 | 94.06 | RNA-G335 | 87.77 | 93.36 |
RNA-G251 | -96.81* | 99.17* | RNA-A306 | 96.57 | 99.14 | RNA-G338 | 58.59 | 78.02 |
RNA-G257 | 93.56 | 96.51 | RNA-G317 | 84.47 | 91.60 | RNA-G339 | -93.85* | 98.55* |
RNA-G259 | 95.11 | 97.35 | RNA-G320 | 62.44 | 80.17 | RNA-G340 | 58.67 | 78.19 |
RNA-G261 | 96.06 | 97.87 | RNA-A326 | 92.93 | 96.13 | RNA-G344 | 73.39 | 85.85 |
RNA-C267 | -99.24* | 99.86* | RNA-A327 | 99.35 | 99.67 | RNA-A356 | 99.60 | 99.80 |
RNA-A268 | -46.31* | 79.05* | RNA-G328 | 91.63 | 95.46 | RNA-A359 | 99.46 | 99.73 |
RNA-A269 | 96.94 | 98.35 | RNA-G329 | 89.54 | 99.33 | |||
RNA-A276 | -96.63* | 99.49* | RNA-A330 | 99.57 | 97.77 | |||
Training Set (Nucleotides ‘footprinted’) | ||||||||
RNA-G214 | -98.79 | 99.37 | RNA-G265 | -44.42 | 71.41 | RNA-G321 | -92.24 | 95.90 |
RNA-C218 | -97.21 | 98.53 | RNA-G266 | -92.87 | 96.14 | RNA-C322 | -98.44 | 99.18 |
RNA-C219 | -98.90 | 99.42 | RNA-A271 | -84.60 | 90.81 | RNA-U323 | -96.61 | 98.22 |
RNA-A220 | -84.39 | 90.90 | RNA-G272 | -98.83 | 95.00 | RNA-A324 | -93.41 | 96.24 |
RNA-G221 | -99.85 | 99.93 | RNA-C274 | -96.61 | 98.20 | RNA-G325 | -99.62 | 99.81 |
RNA-A222 | -84.19 | 90.35 | RNA-G275 | -98.20 | 99.04 | RNA-G342 | -93.34 | 96.53 |
RNA-A225 | -42.56 | 56.29 | RNA-G277 | -98.51 | 99.21 | RNA-C343 | -98.23 | 99.06 |
RNA-C227 | 22.41* | 66.90 | RNA-G282 | -92.64 | 96.01 | RNA-C349 | -98.05 | 98.97 |
RNA-C229 | -98.28 | 99.09 | RNA-G283 | -96.27 | 97.85 | RNA-C352 | -97.26 | 98.50 |
RNA-U230 | -94.75 | 97.26 | RNA-C284 | -98.33 | 99.10 | RNA-G361 | -93.71 | 96.70 |
RNA-C231 | -97.00 | 98.41 | RNA-G285 | -95.59 | 97.58 | RNA-C362 | -99.20 | 99.58 |
RNA-U232 | -38.37 | 68.06 | RNA-C287 | -99.42 | 99.70 | RNA-A368 | -95.09 | 97.19 |
RNA-C233 | -95.44 | 97.56 | RNA-U288 | -88.23 | 93.75 | RNA-A370 | -81.08 | 88.79 |
RNA-C236 | -97.60 | 98.73 | RNA-A293 | -79.98 | 88.22 | RNA-U372 | -5.37 | 51.07* |
RNA-G237 | -94.75 | 97.14 | RNA-G294 | -99.35 | 99.66 | RNA-U377 | -93.70 | 96.61 |
RNA-G246 | -90.80 | 95.03 | RNA-U295 | -96.61 | 98.21 | RNA-C378 | -98.51 | 99.21 |
RNA-C248 | -97.08 | 98.45 | RNA-C297 | -98.11 | 98.99 | RNA-U381 | -92.45 | 96.07 |
RNA-U249 | -94.54 | 97.11 | RNA-G298 | -85.42 | 89.43 | RNA-G382 | -98.74 | 99.34 |
RNA-C252 | -97.80 | 98.83 | RNA-C299 | -96.23 | 97.91 | RNA-G383 | -97.99 | 98.93 |
RNA-U253 | -53.65 | 76.07 | RNA-C307 | -98.35 | 99.12 | RNA-C387 | -97.18 | 98.49 |
RNA-C258 | 67.07* | 88.75* | RNA-U308 | -98.12 | 99.00 | RNA-C388 | -84.47 | 91.70 |
RNA-C262 | 59.31* | 85.25 | RNA-A309 | -85.79 | 91.59 | |||
RNA-C264 | -98.03 | 98.94 | RNA-G310 | -99.10 | 99.53 |
nucleotide | ΔP%a | nucleotide | ΔP%a | nucleotide | ΔP%a |
---|---|---|---|---|---|
Test Set (Nucleotides non-‘footprinted’) | |||||
RNA-A239 | 98.33 | RNA-A286 | -80.84* | RNA-A336 | 99.68 |
RNA-A242 | 97.15 | RNA-C300 | -95.83* | RNA-G346 | 90.17 |
RNA-C245 | 98.23 | RNA-G318 | 90.46 | RNA-A360 | 94.68 |
RNA-G254 | 62.44 | RNA-G331 | 87.67 | ||
Test Set (Nucleotides ‘footprinted’) | |||||
RNA-G213 | -85.46 | RNA-U250 | -97.07 | RNA-G348 | -97.29 |
RNA-G226 | -21.29 | RNA-G273 | 35.31* | RNA-G369 | -99.76 |
RNA-U228 | -87.28 | RNA-C311 | -97.87 | RNA-U373 | -92.40 |
RNA-C238 | -98.32 | RNA-U341 | 47.94* |
N = 23 R = 0.96 R2 = 0.92 s = 0.07 q2 = 0.85 scv = 0.09 F(4.18) = 54.910 p<0.0000
+0.083(±0.035) 4O(Θ8)
N = 24 R = 0.91 R2 = 0.83 s = 0.115 q2 = 0.825 F(3.20) = 31.48 p<0.0000
NUC | Obsa | Predb | P-cvc | Predd | P-cvf | NUC | Obsa | Predb | P-cvc | Predd | P-cvf |
---|---|---|---|---|---|---|---|---|---|---|---|
A235 | 1.204 | 1.132 | 1.111 | 1.166 | 0.359 | G335 | 0.845 | 0.852 | 0.853 | 0.862 | 0.845 |
A239 | 1.204 | 1.173 | 1.164 | 1.166 | 0.359 | G338 | 0.778 | 0.736 | 0.732 | 0.672 | 0.778 |
G251 | 0.447 | 0.350 | 0.304 | 0.518 | 0.032 | G339 | 0.778 | 0.647 | 0.566 | 0.545 | 0.778 |
G254 | 0.447 | 0.552 | 0.578 | 0.518 | 0.032 | G340 | 0.778 | 0.734 | 0.730 | 0.672 | 0.778 |
C267 | 0.903 | 0.893 | 0.879 | 0.856 | 0.058 | G344 | 0.845 | 0.814 | 0.811 | 0.735 | 0.845 |
A268 | 0.903 | 1.003 | 1.049 | 0.856 | 0.125 | G346 | 0.845 | 0.855 | 0.856 | 0.862 | 0.845 |
A269 | 0.903 | 0.984 | 1.026 | 0.987 | 0.125 | G363 | 0.415 | 0.488 | 0.522 | 0.399 | 0.415 |
A286 | 0.778 | 0.704 | 0.667 | 1.024 | -0.067 | G364 | 0.415 | 0.477 | 0.495 | 0.399 | 0.415 |
G328 | 0.845 | 0.851 | 0.852 | 0.862 | 0.430 | G365 | 0.415 | 0.542 | 0.564 | 0.399 | 0.415 |
G329 | 0.845 | 0.852 | 0.853 | 0.862 | 0.430 | G366 | 0.415 | 0.394 | 0.386 | 0.594 | 0.415 |
G331 | 0.845 | 0.852 | 0.853 | 0.862 | 0.430 | G367 | 0.415 | 0.378 | 0.369 | 0.594 | 0.415 |
G333 | 0.845 | 0.852 | 0.853 | 0.862 | 0.845 |
f2q3L(xm) | ΔE1q0L(xm) | ΔE1q10L(xm) | ∈250q3L(xm) | |
---|---|---|---|---|
f2q3L(xm) | 1 | -0.55 | -0.68 | -0.41 |
ΔE1q0L(xm) | 1 | 0.37 | 0.17 | |
ΔE1q10L(xm) | 1 | -0.31 | ||
∈250q3L(xm) | 1 |
Concluding Remarks
Acknowledgements
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Ponce, Y.M.; Nodarse, D.; Díaz, H.G.; De Armas, R.R.; Zaldivar, V.R.; Torrens, F.; Castro, E.A. Nucleic Acid Quadratic Indices of the “Macromolecular Graph’s Nucleotides Adjacency Matrix”. Modeling of Footprints after the Interaction of Paromomycin with the HIV-1 Ψ-RNA Packaging Region. Int. J. Mol. Sci. 2004, 5, 276-293. https://doi.org/10.3390/i5110276
Ponce YM, Nodarse D, Díaz HG, De Armas RR, Zaldivar VR, Torrens F, Castro EA. Nucleic Acid Quadratic Indices of the “Macromolecular Graph’s Nucleotides Adjacency Matrix”. Modeling of Footprints after the Interaction of Paromomycin with the HIV-1 Ψ-RNA Packaging Region. International Journal of Molecular Sciences. 2004; 5(11):276-293. https://doi.org/10.3390/i5110276
Chicago/Turabian StylePonce, Yovani Marrero, Delvin Nodarse, Humberto González Díaz, Ronal Ramos De Armas, Vicente Romero Zaldivar, Francisco Torrens, and Eduardo A. Castro. 2004. "Nucleic Acid Quadratic Indices of the “Macromolecular Graph’s Nucleotides Adjacency Matrix”. Modeling of Footprints after the Interaction of Paromomycin with the HIV-1 Ψ-RNA Packaging Region" International Journal of Molecular Sciences 5, no. 11: 276-293. https://doi.org/10.3390/i5110276