Mathematical [math] methods, soft, data science and their physical application

Advance techniques and Physical Applications provides a wide range of basic math concepts and methods, which are relevant to biophysic theory and biomolecule. This page is devoted to the physical and mathematical modeling of the formation of complexes of protein molecules, antibody and amyloid peptide (alzheimer desease). Real techniques show remarkable sensitivity to the amino acid sequences of proteins, which facilitates experimental studies in lab and allows one to reduce the associated costs by reducing the number of measurements required according to the developed criteria in experimental lab. These models make it possible to reach a conclusion about the interactions between different amino acid chains and to identify more stable sites on proteins via control techniques, soft and Data Science. The models also take the phosphorylation of amino acid residues into account.
You can free download soft for antibody cost saving and learn Data Scince
What is hydrophobic interaction?
The most common explanation is that hydrophobic molecules "do not like" to interact with the aqueous environment. We obtained the values of hydrophobic interactions, calculated their value, developed a method for determining the range of interactions, and developed a graphical representation using soft, math, data science. You can free download soft and learn Data Scince
hydrophobic interactions
hydrophobic interaction
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Biophysics and application in molecular biology

Molecular biophysics is the study of the physical principles governing biomolecular systems. It seeks to explain biological function in terms of molecular structure, dynamics and organization, from single molecules to supramolecular structures.
The epidermal growth factor receptor (EGFR) is often considered the “prototypical” receptor tyrosine kinase (RTK) and has been intensively studied. It is one of a family of four RTKs in humans, the others being ErbB2/HER2, ErbB3/HER3, and ErbB4/HER4
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Most people have relatives or friends who are sick or who have already left us. In 2017, 9.6 million people are estimated to have died from the various forms of cancer. Every sixth death in the world is due to cancer, making it the second leading cause of death — second only to cardiovascular diseases.
And it is in our power to do everything possible to combine our efforts in order to increase the life expectancy of cancer patients until their full recovery, as well as improve their quality of life by increasing the selectivity and effectiveness of drugs and reducing their toxicity.

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Our method is molecularly selective, targeting certain oncogenic molecules, namely the EGFR family of tyrosine kinases, which occupy a significant share in the causes of oncogenic diseases. The diagram shows the percentage of mutations in proteins of the EGFR family in non-small cell lung cancer

Amyloid plaques. Alzheimer's disease

Structure and Aggregation Mechanisms in Amyloids

Biophysical method for inhibiting amyloid plaques developed by our group. Amyloid fibrils are formed by normally soluble proteins, which assemble to form insoluble fibers that are resistant to degradation. Amyloids is a collective term to describe misfolded proteins that self-assemble into insoluble fibrils both in vitro and in vivo. Why do some amyloids cause serious neurodegenerative diseases, while others have important biological functions?
A Graphical User Interface for Alanine Scanning

Computer alaning scaning

Here, we present an accurate computational scheme to predict and interpret the effects of alanine scanning. Substitution with alanine residues eliminates side-chain interactions without altering main-chain conformation or introducing steric or electrostatic effects, so is often the preferred choice for testing the contribution of specific side-chains while preserving native protein structure.

Protein-protein interactions. Miscellaneous.

Examples of various calculations taking into account three-dimensional structure, as well as without taking into account three-dimensional structure
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Behind the big data

Linear Docking

An alternative method to molecular docking, which could widely used in molecular biology, biophysics, drug design. We use this method for protein-protein interactions and protein docking for searching active site of proteins.
For modern proteomics, research and prediction of protein-protein interactions are very important tasks, since they determine the function of proteins at levels from the cell to the whole organism, allowing you to find active sites of interaction. For proteins whose structure is known, the search for intermolecular interactions according to known data on the conformation of their tertiary structure reduces to the problem of searching for geometric complementarity of the sections of two interacting molecular surfaces and modelling their contacts, the so-called molecular docking [System Computer Biology . Monograph. Novosibirsk: Publishing House of the SB RAS.2008.769 p].
Modern Proteomics – Sample Preparation, Analysis and Practical Applications
novel proteomic and strategies
Modern conformational search algorithms in most cases find conformations that are generall close to the experimentally found structures in a relatively short time. However, there are factors that also have a significant impact on the success of the docking, which are often not taken into account in standard algorithms. One such factor is the conformational mobility of the target protein. The mobility range can be different beginning with a small «adjustment» of the side chains and ending with scale domain movements [Betts M.J., Sternberg M.J. An analysis of conformational changes on protein-protein association: implications for predictive docking.// Protein Eng. 1999. V. 12. Pp. 271-283]
Direct Activation of Bax Protein for Cancer Therapy Bax Protein for Cancer Therapy
Bax Protein for Cancer Therapy
These movements play an important role. At the same time, for each rotation configuration, estimates are made for the evaluation function.
The evaluation function is based on surface complementarity (the mutual correspondence of complementary structures (macromolecules, radicals), determined by their chemical properties), electrostatic interactions, van der Waals repulsion, and so on. The problem with this approach is that calculations throughout the configuration space require a lot of time, rarely leading to a single solution, which in turn does not allow us to speak of the uniqueness of the target protein and ligand interaction variant. So, while modelling by the methods of molecular dynamics, from 200 to 10 000 possible combinations of the formation of a protein complex with a ligand were found.
Numerical calculations were made using proteins Mdm2, Nap1, P53. For modern proteomics, research and prediction of protein interactions are very important .
Numerical calculations were made using proteins Mdm2, Nap1, P53
Such a large number of modifications, along with the lack of a criterion for selecting the most probable variants of the bound structures of biological complexes (which would allow a radical reduction in their number) makes it very difficult to interpret the theoretical results obtained for practical use, namely, the finding of catalytic centers and a qualitative assessment of the dissociation constant of interacting substances.

In contrast to the above computer simulation algorithms, mathematical algorithms have been developed in this soft that allow determining the detection of proteins active regions and detecting the stability of different regions of protein complexes (linear docking) by analyzing the potential energy matrix of pairwise electrostatic interaction between different sites of the biological complex.

At first glance, the most logical solution to this problem is to take into account the mobility of the protein in a docking program. Unfortunately,modern computational tools do not allow such modelling to be performed in an acceptable time frame since a protein molecule is very large, and allowing for mobility over all degrees of freedom can lead to a so-called «combinatorial explosion» (an astronomical increase in the number of possible variants). Only in some programs is there a limited mobility of protein binding sites (usually at the level of a small adaptation of conformations of the side chains of the active center residues). Another approach to this problem consists in docking the same protein in several different conformations and then selecting the best solutions from each docking run. The third approach is to find a universal structure of the target protein in which docking would produce fairly good results for different classes of ligands. In this case, the number of «missed» (but correct) solutions decreases, but the number of incorrect options [Pyrkov T.V., Ozerov I.V., Balitskaya E.D., Efremov R.G. Molecular docking: the role of non-valence interactions in the formation of protein complexes with nucleotides and peptides// Bioorganic Chemistry 2010. V.36. N4. Pp.482-492] also increases significantly. It should also be noted that most programs for the theoretical docking of proteins work according to the following principle: one protein is fixed in space, and the second is rotated around it in a variety of ways.

The proposed theoretical method allows one to take into account the change in the stability of the biological complex with point mutations in proteins, as well as to obtain information about the distribution of the potential energy of electrostatic interaction, indicating the location of key amino acid residues during the formation of the biological complex. Based on a visual map of the interaction of two proteins, which is obtained on the basis of our
method, we can determine whether the complex is stable when replacing key amino acid residues, which in turn will coincide qualitatively with the experimental Kd measured value. Thus, the analysis of the results allows us to identify amino acid residues that play a significant role in the formation of a biological complex.

Also the developed and physically grounded mathematical approach, in addition to work on molecular dynamics, will theoretically predict the passage of the biochemical reaction in the selected direction with the given amino acid sequences, identify the stability of different areas of protein complexes by analyzing the potential energy matrix of electrostatic interaction between different sites of the biological complex, and also examine the effect of point mutations in BH3 peptides on the stability of the biological complex formed by them with the proapoptic proteins of the Bcl-2 family and qualitatively determine the dissociation constants when different BH3 peptides bind to the Bcl-2 proteins.

The developed software package will allow:

to determine the key amino acid residues in the protein complex, which account for the maximum values of the potential energy of electrostatic interaction;

to determine the effect of point mutations in peptides on the stability of the resulting biological complexes with protein. To qualitatively determine the range of variation of Kd during point mutations, when peptides bind to the active protein site;

to determine the active sites of the interactions between proteins, when it is formed in succession of a.a. residues of two proteins with an unknown three-dimensional structure of proteins.

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