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Step-by-step approaches in checking the correctness of building 3D structures (PDB files)

Selection of PDB structures to be analyzed.

Pick up the structures of biological molecules (possibility of adding inhibitors). In the case of selecting several structures, the following options are possible:**1)**All PDB structures are executed correctly**2)**Some of the structures are correct, some are not.**3)**All selected PDB structures are not executed correctly.- RMSDDependence of
**RMSD**(root-mean-square deviation) on the configuration number. Performing this calculation for all selected PDB structures, finding a minimum or not finding one. - Calculation error analysisThe calculated error should be much smaller than the results obtained.
Comparison of calculation results among themselves.

Performing a stability calculation for all selected PDB structures, taking into account the same modification in the PDB structures.**Agreement between the obtained results.**Comparison of calculation results with experimental data

Comparison of all obtained calculated data with experimental values, if any.

X-Ray structure analysis.

Algorithms for checking the structure PDB

Algorithms for checking the structure PDB

The algorithm for checking the structure PDB consists in In finding an optimized cost function for a specific PDB structure, and also estimate of the computational error of the singular value decomposition.

E

_________________**number condition** ______**_****max** _____________**min**___________________**error comput. SVD**

**(1)3d4q** ______________5.12875_______________ _4.468e-19_______ 3.322e-24________________ __**1.5019e-19**

**(2)3d4q(dimer****)**_ __21.7414 _______________ 1.568e-19_________**2.8440e-41**_________________9.081e-34

**(3)2MXU***__________5.5372 _____________ ___**5.819e-20****_________****1.6892e-25 ****________________****5.345e-35**

**(4)5KK3*****___________**6.21113__________________**5.729e-20**________**3.523e-26**__________________**6.994e-35**

_____max RMSD__________First-Order Optimaly Measure

3.33874663756617e-13_________4.42060133588067e-07

3.33874663756617e-13_________4.42060133588067e-07

3d4q(monomer)

(1)3d4q

(2 prot.+2 chem)

(2 prot.+2 chem)

(3)2MXU

(2amyloid peptides)

(2amyloid peptides)

(2)3d4q(dimer)

If an optimized cost function for a specific PDB structure is not found, then we consider that this structure is formed incorrectly. Also for analysis structures we use the root maean squared deviation (RMSD).

Figure 3: Dependence of RMSD(root-mean-square deviation) on the configuration number

The fig.1 shows a rapidly oscillating character, which indicates the impossibility of finding a local minimum: optimization completed because at the initial point, the objective function is nondecreasing in feasible directions. As follows from the fig.1 the local minimum no found.

N1-modified pyrazole

B-Raf IC50 (nM)

0.03

IC50 values reflect the average from at least three separate experiments.

B-Raf

B-Raf

B-Raf

pyrazole

pyrazole

B-Raf

B-Raf

amyloid pep1

amyloid pep2

the impossibility of finding a local minimum

*The calculation data for amyloid dimers is given here as an example of normal relationships between vibrational modes, **number condition** and **error SVD**.

Computational error**1.5019e-19** is too large compared to the

obtained values**3.322e-24**

Computational error

obtained values

2.

3.

Table №2

Number

PDB

Explanation

Pyrazole-based inhibitors of B-Raf kinase

1.

3d4q

error computational SVD 1.5019e-19

Figure 1.Chemical three-dimensional structures of a small chemical molecule.

3d4q

3d4q

Table №1

The results of the performed calculations for these three-dimensional structures do not allow at this stage to carry out further studies in order to determine the shift in thermodynamic equilibrium. Either comparison with a similar structure or direct agreement with experimental data is required.

Dependence of RMSD(root-mean-square deviation) on the configuration number.

Determination of the computational error of the SVD

Comparison of calculated data for two identical PDB structures.

In the next section, various examples are given, taking into account the correlation of the two previous parameters, as well as the experimental correlation of the results and the comparison of the PDB structures with each other based on the comparability of the calculated data. This section lists some of the key points of checking the PDB structure, for more detailed information, contact the developers personally, or check out the relevant publications.

As can be seen from the above graphs, the results of the experimental and numerical calculations are in good agreement, and the most stable amyloid altered complex is the formation of a biological complex involving amyloid peptides, in which 4 amino acid substitutions were made in each peptide **18SER, 21SER, 40SER, 42SER**

Comparison of experimental and calculated data.

We proposed a new method that can explain the formation of high-

molecular-weight amyloid structures in terms of the stability of amyloid complexes and performed numerical grading for a three-dimensional structure from the PDB database in terms of the stability of amyloid dimers. For biocomplexes which consist of such dimers we identified a numerical value of**lg(cond(W)) = 5.53** as a threshold value of the biocomplex stability. This value arbitrarily distinguishes dimers with reduced propensity to form high molecular-weight structures from those with elevated propensity. A value of **5.53** was found previously from analysis of experimental data on mutations in amyloid peptides, their physiological and biophysical properties, and the ability to participate in ever biochemical reactions

molecular-weight amyloid structures in terms of the stability of amyloid complexes and performed numerical grading for a three-dimensional structure from the PDB database in terms of the stability of amyloid dimers. For biocomplexes which consist of such dimers we identified a numerical value of

3.

4.

Table №2

Number

PDB

Explanation

42-Residue Beta Amyloid Fibril

Structure of Monomorphic AB42 Amyloid Fibrils

Structure of Monomorphic AB42 Amyloid Fibrils

1.

2MXU

5KK3

5KK3

error computational SVD **5.3455e-35**

2MXU

5KK3

5KK3

2MXU

5KK3

5KK3

2MXU

5KK3

5KK3

5.

error computational SVD **6.9947e-35**

Good correletions

Good correletions

Good correletions.

not tested

All calculations were performed using this pdb

Detailed information on the calculation of amyloid peptides

Lack of agreement in the resulting calculations for two identical biological molecules whose structures were obtained in different laboratories

4.7322

4.61146

4.0289e-19

4.16581e-19

7.463e-24

1.0191e-23

2Y4I

7JuQ

Figure 1: Dependence of RMSD(root-mean-square deviation) on the configuration number

a)

b)

The fig.1 shows a rapidly oscillating character, which indicates the impossibility of finding a local minimum: optimization completed because at the initial point, the objective function is non-decreasing in feasible directions.

impossibility of finding a local minimum

Анализ и сопоставление величин колебательных мод, condition number and error SVD

The resulting computational error **2.644e-19** is much larger than the lower vibrational mode **7.463e-24** and is comparable with the calculation results for the upper vibrational mode **4.028e-19** for two structures

PDB:2Y4I

PDB:7JUQ

7JUQ

2Y4I

lack of correlation in the obtained calculations

Figure 2. Structures of the two studied PDB files 2Y4I and 7JUQ

Figure 3. The results of numerical calculations performed for two different PDBs containing the same structures and the same amino acid residue substitutions.

2.

3.

4.

No correletions

Table №2

Number

PDB

Explanation

KSR2-MEK1 heterodimer (+ADP)

Crystal Structure of KSR2:MEK1 in complex with ADP

Crystal Structure of KSR2:MEK1 in complex with ADP

1.

2Y4I

7JUQ

7JUQ

2Y4I

7JUQ

7JUQ

2Y4I

7JUQ

7JUQ

2Y4I

7JUQ

7JUQ

No correletions

error computational SVD **2.5450e-19**

error computational SVD **2.6446e-19**

Dependence of RMSD(root-mean-square deviation) on the configuration number.

Table №1

As can be seen from the results of the performed calculations, we did not receive a single satisfactory result for the three points of verification.

Figure 2. **Chemical structures of Erlotinib-EGFR dimer with indication of key amino acid residues**

PDB: 1M17

The first graph (

The numerical results correspond well to the previously obtained IC50 values; namely, the L858R substitutions in EGFR lead to a decrease in the two values of IC50 and lg(cond(W)) when interacting with erlotinib. The double substitution of T790M/L858R in EGFR leads to an increase in the experimental and calculated values of IC50 and lg(cond(W)). At the same time, we interpret the increase in lg(cond(W)), when the system switches from the wild-type to a mutant form of mEGFR (T790M/L858R)-erlotinib as a decrease in dimer stability which is reflected in the decrease in the affinity of the mutant form of the protein to erlotinib.

f(x)

9.056660e-19 7.560563e-09 7.561525e-09

9.056660e-19 7.560563e-09 7.561525e-09

Feasibility

0.000e+00

0.000e+00

0.000e+00

0.000e+00

0.000e+00

0.000e+00

First-order optimality

1.983e-06

3.982e-01

3.948e-01

1.983e-06

3.982e-01

3.948e-01

Norm of step

1.599e-07

5.456e-10

1.599e-07

5.456e-10

Iter

1

2

3

1

2

3

F-count

1

34

36

1

34

36

Finding the minimum of constrained nonlinearmultivariable function

From table follow value local minimum (fmin = 7.561525e-09) and so, **structure PDB:1M17 is formed correctly**. If an optimized cost function for a specific PDB structure is not found, then we consider that this structure is formed incorrectly (see fig. 1)

The fig.1 shows a rapidly oscillating character, which indicates the impossibility of finding a local minimum: optimization completed because at the initial point, the objective function is non-decreasing in feasible directions.

Figure 1: Dependence of RMSD(root-mean-square deviation) on the configuration number

number condition

5.408507761

5.408613530

5.407063570

5.408507761

5.408613530

5.407063570

max eigenvalue

7.2105e-20

7.2125e-20

7.1860e-20

7.2105e-20

7.2125e-20

7.1860e-20

min eigenvalue

2.8149e-25

2.8149e-25

2.8146e-25

2.8149e-25

2.8149e-25

2.8146e-25

error computational SVD

**2.2197e-34**

**2.0642e-34**

**2.17951e-34**

L858R

RT790M/L858R

number condition

5.84513929

5.84442578

5.86249425

5.84513929

5.84442578

5.86249425

max eigenvalue

6.2412413e-20

6.2464520e-20

6.2121049e-20

6.2412413e-20

6.2464520e-20

6.2121049e-20

min eigenvalue

8.9152121e-26

8.937326e-26

8.52598e-26

8.9152121e-26

8.937326e-26

8.52598e-26

error computational SVD

**1.18927e-34**

**1.99404e-34**

**1.26733e-34**

L858R

RT790M/L858R

impossibility of finding a local minimum

PDB: 4HJO

PDB: 4HJO

PDB: 1M17

Table №2

Table №3

PDB: 1M17

PDB: 4HJO

Determination of the computational error of the SVD

Dependence of RMSD(root-mean-square deviation) on the configuration number.

4. Comparison of calculated data of two structures 1M17 and 4HJO.

5. Comparison of experimental and calculated data.

5. Comparison of experimental and calculated data.

2.

1M17

4HJO

4HJO

1M17

4HJO

4HJO

error computational SVD 1.189e-34

error computational SVD 2.219e-34

3.

4.

1M17/4HJO

No correletions

5.

1M17

4HJO

4HJO

Table №4

Number

PDB

Explanation

EGFR tyrosine kinase domain with inhibitor erlotinib

EGFR tyrosine kinase domain with erlotinib

EGFR tyrosine kinase domain with erlotinib

1.

1M17

4HJO

4HJO

Good correletions

No correletions

Table №1

The experimental values were taken *[In vitro modeling to determine mutation specificity of EGFR tyrosine kinase inhibitors against clinically relevant EGFR mutants in non-small-cell lung cancer]*