MelroLeandro / Protein-periodicity

A coarse grained circular statistical tool that allows us to estimate the role of local and nonlocal factors in determining both the secondary and tertiary structure of globular proteins.

Protein periodicity ---

http://melroleandro.github.io/Protein-periodicity/

This is the base for a project on packing charged multibody systems with implicit solvation. This scripts are used for the extraction of statistical dada from large samples of crystal structures, selected from the PDB. The generated statistics are used on two type of libraries for multibody dynamics: a library with statistical potentials for pairs of dihedral angles in the main chain local conformation, and a rotamer libraries. This libraries are defined as a set of discrete probability distribution, and used to generat internal forces multibody systems.

• Examples of statistical potentials generated from two dihedral angles on a protein main chain:

• Examples of statistical potentials generated between dihedral angles and rotamers in an amino acid:

For more information: http://melroleandro.github.io/Protein-periodicity/

Extraction of Statistic for each amino acid

For Amino TYR

SAMPLE SIZE: 1615

	B-factor
Mean	18.34
Median	15.38
Variance	144.59
Standard deviation	12.02
Skewness	2.73
Kurtosis	15.87

	C-CA	N-CA	peptid plane
Mean	2.08	1.79	1.60
Median	1.53	1.46	1.33
Variance	1.50	0.77	0.54
Standard deviation	1.23	0.88	0.73
Skewness	2.00	2.85	3.07
Kurtosis	5.47	10.28	12.80
corrcoef	1.00	0.67	0.22
corrcoef	0.67	1.00	0.15
corrcoef	0.22	0.15	1.00

	PHI	PSI
Mean	-89.45	111.99
Median	-88.90	122.94
R Length	0.48	0.14
Variance	0.52	0.86
Standard deviation	1.02	1.31
Standard deviation 0	1.21	1.97
Skewness	-0.10	0.48
Kurtosis	0.34	0.18

Inferential Statistics for $$\phi$$-$$\psi$$

Tests for Uniformity

• Rayleigh Test, P = 0.00 0.00
• Omnibus Test, P = 0.00 0.00
• Rao Spacing Test, P = 0.50 0.50
• V Test (r = 0), P = 0.40 1.00

Measures of Association $$\phi$$-$$\psi$$

Circular-Circular Association

• Circ-circ corr phi-psi coeff/pval: -0.22 0.000
• Circ-line corr phi-C-CA coeff/pval: 0.65 0.000
• Circ-line corr phi-N-CA coeff/pval: 0.43 0.000
• Circ-line corr psi-C-CA coeff/pval: 0.32 0.000
• Circ-line corr psi-N-CA coeff/pval: 0.21 0.000

Statistics $$\chi_1$$

	CHI_1
Mean resultant vector	108.13
Median	108.13
R Length	0.05
Variance	0.95
Standard deviation	1.38
Standard deviation 0	2.41
Skewness	-0.00
Kurtosis	0.00

Inferential Statistics $$\chi_1$$

Tests for Uniformity

• Rayleigh Test, P = 0.01
• Omnibus Test, P = 0.05
• Rao Spacing Test, P = 0.50
• Circ-circ corr phi-chi1 coeff/pval: 0.00 0.850
• Circ-circ corr psi-chi1 coeff/pval: 0.04 0.141

Statistics $$\chi_2$$

	CHI_2
Mean resultant vector	-86.02
Median	-86.02
R Length	0.38
Variance	0.62
Standard deviation	1.11
Standard deviation 0	1.38
Skewness	0.27
Kurtosis	0.19

Inferential Statistics $$\chi_2$$

Tests for Uniformity

• Rayleigh Test, P = 0.00
• Omnibus Test, P = 0.00
• Rao Spacing Test, P = 0.50
• Circ-circ corr phi-chi2 coeff/pval: -0.16 0.000
• Circ-circ corr psi-chi2 coeff/pval: 0.06 0.011
• Circ-circ corr chi1-chi2 coeff/pval: 0.01 0.776

Statistics $$\chi_3$$

	CHI_3
Mean resultant vector	11.78
Median	11.78
R Length	0.24
Variance	0.76
Standard deviation	1.23
Standard deviation 0	1.68
Skewness	0.25
Kurtosis	-0.63

Inferential Statistics $$\chi_3$$

Tests for Uniformity

• Rayleigh Test, P = 0.00
• Omnibus Test, P = 0.00
• Rao Spacing Test, P = 0.50
• Circ-circ corr phi-chi3 coeff/pval: 0.00 0.983
• Circ-circ corr psi-chi3 coeff/pval: -0.01 0.788
• Circ-circ corr chi1-chi3 coeff/pval: 0.00 0.960
• Circ-circ corr chi2-chi3 coeff/pval: -0.36 0.000

$$\phi$$ & $$\psi$$

$$\chi_1$$

$$\chi_2$$