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The goal of our work is to create a method that would allow experimenters to obtain visual physical characteristics of biochemical reactions in an understandable accessible format.
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At the same time, we set ourselves the goal that the obtained data could be directly compared with the data obtained in an in vitro experiment. Let's move on to an example in which the affinity was obtained independently using experimental equipment and using our software.
The purpose of our software development is to predicte the affinity of a biological complex, which is comparable to such experimental values as Kd (a specific type of equilibrium constant), IC50 (the half maximal inhibitory concentration ), ΔH, potential energy of interaction.
Modeling the impact of point mutations on the stability of proteins. EXAMPLE 1 BIOLOGICAL SOFT
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Next, we will demonstrate examples of the application of the developed software in the field of virology. This is only one of the areas of use of the developed biophysical concept and the corresponding set of tools.

The contribution of
point mutations to the affinity of a dimeric protein complex

ACE2- (S) -glycoprotein dimeric complex was investigated and also research the identification of key amino acid residues in the ACE2 protein when binding to the SARS-CoV-2 virus
Bellow we present the results of mathematical simulation of the the contribution of point mutations to the affinity of a dimeric protein complex. As an example, the ACE2- (S) -glycoprotein dimeric complex was investigated and research the identification of key amino acid residues in the ACE2 protein when binding to the SARS-CoV-2 virus Spike-glycoprotein viral protein; the replacement of amino acid residues in the ACE2 protein in the alfa-helical region on the N-end side that participate in binding to the (S) glycoprotein was performed.
The method developed allows us to analyze the change in the affinity of a dimeric protein complex during mutations in the region of the active center in any of the proteins. The results obtained are in good agreement with the methods in [Stawiski E.W., Diwanji D. et al. Human ACE2 receptor polymorphisms predict SARS-CoV-2 susceptibility //BioRxiv 2020, doi: https://doi.org/10.1101/2020.04.07.024752.]

Introduction
The recent pandemic of COVID-19, caused by SARS-CoV-2, is unarguably the most fearsome compared with the earlier outbreaks caused by other coronaviruses, SARS-CoV and MERS-CoV. Human ACE2 is now established as a receptor for the SARS-CoV-2 spike
protein
[1]. SARS-CoV and SARS-CoV-2 spike proteins interact with human angiotensinconverting enzyme 2(ACE2) as their receptor [1]. It has been shown that variations in both viral spike protein and host ACE2 sequences may act as a barrier for viral infection across species [2]−[4]. Structural variations inhuman ACE2 may influence its binding with SARS-CoV-2 spike protein [1]. Angiotensin converting enzyme-2 (ACE2) receptors mediate the entry into the cell of three strains of coronavirus: SARS-CoV, NL63 and SARS-CoV-2. ACE2 receptors are ubiquitous and widely expressed in the heart, vessels, gut, lung (particularly in type 2 pneumocytes and macrophages), kidney, testis and brain. ACE2 is mostly bound to cell membranes and only scarcely present in the circulation in a soluble form [5].
The entry of SARS-CoV-2 into cells is mediated by the efficient binding of the spike (S) viral protein, a 1273 amino acid long protein which belongs to the viral envelope and protrudes outwards with a "corona" like appearance, to the angiotensin converting enzyme 2(ACE2) receptors [6]−[7]. A recent publication reported the structure of the S protein of SARS-CoV-2 and showed that the ectodomain of the SARS-CoV-2 S protein binds to the PD of ACE2 with a dissociation constant (Kd) of ∼15nmol[8] primary physiological role is in the maturation of angiotensin(Ang), a peptide hormone that controls vasoconstriction and blood pressure. ACE2 is a type I membrane protein expressed in lungs, heart, kidneys, and intestine [9]−[10]. Decreased expression of ACE2 is associated with cardiovascular diseases [11]−[13]. Full-length ACE2 consists of an N-terminal PD and a C-terminal collectrin-like domain (CLD) that ends with a single transmembrane helix and a ∼40-residue intracellular segment [14]−[15].

In this chapter, the key amino acid residues of the ACE2 protein were identified, the replacement of which affects the stability of the spike-glycoprotein-ACE2 dimer complex.


For this purpose, various substitutions of the amino acid residues of the ACE2 protein from 21 a.a. to 38 a.a. were performed in the region of binding to the spike-glycoprotein. The stability analysis of the modified protein dimer was carried out according to three criteria. A conclusion was drawn on the effect of each substitution on the affinity of the biological complex.
The purpose of the method developed in the article is to determine modifications of the polypeptide chain that increase the stability of the dimer complex. Modifications that lead to a decrease in the stability of the dimer complex are not of interest to us, since the general aim of this biophysical model is to find stable dimers and their further application in the development of new antibodies.
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Fig.1.Interactions between SARS-CoV-2- and ACE2. The ACE2 mainly engages the alfa-helix in the recognition of the spike-glycoprotein.
Fig. 1. shows the site of interaction of the two proteins SARS-CoV-2 and ACE2, which we will study, namely, the alfa-spiral site from 24 a.a. to 38 a.a. We simulated the substitution of amino acid residues in the wild type Ace2 protein in the alfa-helix region and analyzed the influence of such substitutions on the change in stability of the protein complex Ace2-(S)-glycoprotein.
In the process of analyzing changes in the interaction of two proteins during dimer formation, we will analyze two values that characterize the stability of the protein complex.
1.The condition number condition number of the matrix the elements of which are potential energies of electrostatic interaction between pairs of amino acid residues in proteins.

2. For a more accurate estimate characterizing the stable state of the biological complex, it is necessary to correlate the parameter lg(cond(W))with the change in the differential
entropy measure

Moreover, if the first quantity lg(cond(W)) is characterized by the minimum value, and the second (delta) H by a negative value, and the observed dynamics of change (transformation) of these two quantities occur simultaneously (synchronously), then this will indicate a transition of the biological system to a more stable state.

Numerical calculation results

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Figure 2: Three-dimensional representation of the potential energy of interaction between paired amino acid residues of two Ace2 and spike-glycoproteins. Blue indicates interactions
of hydrophobic amino acid residues, green indicates interactions of hydrophilic amino acid residues, and red indicates interactions of charged amino acid residues. The figures above the bars indicate some values of the potential energy of the electrostatic interaction
between the two proteins.

Figure 2 shows a three-dimensional representation of the potential energy of electrostatic interaction between the amino acid residues of two Ace2 and spike-glycoproteins. As the figure shows, the potential energy value 7.28−21 J is the maximum positive value on the represented map section. The PDB:6VW1 structure was used for calculations. Thus we can see the change in physical parameters of dimer complex formation upon replacement amino acid residues in the ACE2 protein.

Fig. 3 shows the results of numerical calculations for the alternate replacement of I21V(ILE21VAL), E23K(GLU23LYS), K26R (LYS26ARG), N33I(ASN33ILE), H34R (HIS34ARG), E35K(GLU35LYS) , E37K(GLU37LYS), D38V (ASP38VAL), we calculated such quantities as lg(cond(W)) and (delta)H for each modified dimeric complex ACE2-(S)-glycoprotein.

To analyze the results that allow substitutions of amino acid residues in protein polypeptide chains - corresponding to an increase in the affinity of the dimeric complex to be found, we used criteria that together indicate an increase in the affinity of the dimeric complex:
1. the value of lg(cond(W)) demonstrates a decrease in the transition from the interaction of wild-type proteins to mutant forms of interacting proteins;
2. the value of (delta)H is in the range of negative values for the comparison of two dimers;


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Figure 3: Graphical representation of the dependence of the value of lg(cond(W)) on the replacement of the amino acid residue in the ACE2 protein when binding to S-glycoprotein a),graphical representation of the dependence of the value of ¢H on the replacement of amino acid residue in ACE2 protein when binding to S-glycoprotein b), Identified polymorphisms in human ACE2 mapped to the structure of human ACE2 in complex with the SARS-CoV-2 RBD. Residues in ACE2 showing polymorphic variation in human population were mapped on to the structure of the ACE2/SARS-CoV-2 RBD (PDB: 6VW1) and colored according to their effect on the predicte [16] c).Green ticks indicate modifications of the ACE2 protein that increase the stability of the dimer complex and red crosses indicate modifications that are unsuitable for increasing the stability of the dimer complex.

Conclusions

The developed method allows us to take into account the effect of mutations in the polypeptide chain of a protein in the region of the active site of binding to another protein on the stability of the dimeric complex. Thus, the proposed method allows us to obtain data on the stability of the dimeric complex during various mutations in the polypeptide chain of proteins.
In this chapter, we performed a numerical simulation of the substitution of amino acid residues in the alfa-helical section of the ACE2 protein when binding to (S)-glycoprotein.
Replacements of amino acid residues have been identified that affect the increase in stability of the dimeric complex. This approach can be used both for the selection of inhibitors, since we identify amino acid residues the substitutions of which most affect the stability of the dimer complex, and to identify mutations in viral proteins that will
increase or decrease the stability of the dimer complex with human proteins.

There are likely natural variations in ACE2 in human populations, though not under selection, that may increase or decrease its affinity to SARS-CoV-2 S-protein and thereby render individuals more resistant or susceptible to the virus [16].
References
[1] Mushtaq Hussain et al.Structural variations inhumanACE2 may influence its binding with SARS-CoV-2 spike protein//J. Med. Virol. 2020, doi: 10.1002/jmv.25832.
[2] Cui J., Li F., Shi ZL. Origin and evolution of pathogenic coronaviruses.//Nature Reviews Microbiology, 2019, Volume 17,Issue 3, pages 181−192.
[3] Liu Z., Xiao X., Wei X., et al. Composition and divergence of Coronavirus spike proteins and host ACE2 receptors predict potential intermediate hosts of SARSCoV- 2//J. Med. Virol. 2020. https://doi.org/10. 1002/jmv.25726
[4] Wan Y., Shang J., Graham R., Baric R.S., Li F. Receptor recognition by novel coronavirus from Wuhan: an analysis based on decade-long structural studies of SARS//J. Virol. 2020, Volume 94, Issue 7, pages 1−9.
[5] Verdecchia, P., Cavallini C., Spanevello A. and Angelib F. The pivotal link between ACE2 deficiency and SARS-CoV-2 infection.// Eur. J. Intern. Med. 2020, Volume 76, pages 14−20.
[6] Hoffmann M., Kleine-Weber H., Schroeder S., Kruger N., Herrler T., Erichsen S., Schiergens T.S., Herrler G., Wu N.H., Nitsche A., Muller M.A., Drosten C., Pohlmann S. SARS-CoV-2 Cell Entry Depends on ACE2 and TMPRSS2 and Is Blocked by a Clinically Proven Protease Inhibitor//Cell, 2020, Volume 181, Issue 2, pages 271−280. .
[7] Walls A.C., Park Y.J., Tortorici M.A., Wall A., McGuire A.T., Veesler D. Structure, Function, and Antigenicity of the SARS-CoV-2 Spike Glycoprotein//Cell, 2020, Volume 181, Issue 2, pages 281−292.
[8] D. Wrapp et al. Cryo-EM structure of the 2019-nCoV spike in the prefusion conformation// Science, 2020, Volume 367, Issue 6483, pages 1260−1263.
[9] Zhang H., et al. The digestive system is a potential route of 2019-nCov infection: a bioinformatics analysis based on single-cell transcriptomes//BioRxiv 2020, doi: https://doi.org/10.1101/2020.01.30.927806
[10] Zhao Y., et al. Single-cell RNA expression profiling of ACE2, the putative receptor of Wuhan 2019-nCov//BioRxiv 2020, https://doi.org/10.1101/2020.01.26.919985.
[11] Crackower M.A., et al.Angiotensin-converting enzyme 2 is an essential regulator of heart function//2002, Nature Volume 417, pages 822−828.
[12] Zisman L. S., et al. Increased angiotensin-(1-7)-forming Activity in Failing Human Heart Ventricles: Evidence for Upregulation of the Angiotensin-Converting Enzyme Homologue ACE2 //Circulation, 2003, Volume 108, pages 1707−1712.
[13] Raizada M. K., Ferreira A. J., Cardiovasc J. ACE2: A New Target for Cardiovascular Disease Therapeutics.//Pharmacol., 2007, Volume 50,Issue 2, pages 112−119.
[14] (H. Zhang et al. Collectrin, a Collecting Duct-Specific Transmembrane Glycoprotein, Is a Novel Homolog of ACE2 and Is Developmentally Regulated in Embryonic KidneysJ.//Biol. Chem., 2001, Volume 276, Issue 20, pages 17132−17139.
[15] Renhong Y., Yuanyuan Z. et al.Structural basis for the recognition of SARS-CoV-2 by full-length human ACE2//Science, 2020,Volume 367, Issue 6485, pages 1444−1448.
[16] Stawiski E.W., Diwanji D. et al. Human ACE2 receptor polymorphisms predict SARS-CoV-2 susceptibility//BioRxiv 2020, doi: https://doi.org/10.1101/2020.04.07.024752.

Coronavirus (Covid-19) is a world pandemic.
This disease has severely crippled the entire world with the rise of more than 2,000,000 confirmed cases across the global, and a death toll exceeding 170,000. This pandemic Covid-19 touches every aspect of people's lives including one's education, health and of course one's financial situation. With the great hope of finding a cure for this illness, there's naturally an on-going, worldwide effort to identify effective drugs and to develop vaccines

This article describe a detailed method for selecting inhibitors based on modified natural peptides for the SARS-CoV protein spike glycoprotein. The selection of inhibitors is carried out by increasing the affinity of the peptide to the active center of the protein. The article also provides a step-by-step guide to the analysis of affinity of interaction by comparing 3 criteria, presents an analysis of energy interactions between the active center of a protein and the wild-type peptide interacting with it and taking into account modifications of the latter.
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Let us consider in more detail the results of the use of peptides in the inhibition of viral activity.
1. Previously reported SARS-CoV infectivity was reduced over 10,000-fold through pre-incubation with two peptides, while it was completely inhibited in the presence of three peptides.Were reported that four 20-mer synthetic peptides (S protein fragments), designed to span these sequence variation hotspots, exhibited significant antiviral activities in a cell line. [Synthetic peptides outside the spike protein heptad repeat regions as potent inhibitors of SARS-associated coronavirus]

2. Another study reported that Peptide P8 (P2 + P6 + P10) exhibited the strongest antiviral activity, Synergistic antiviral effects mediated by peptide combinations. [Synthetic peptides outside the spike protein heptad repeat regions as potent inhibitors of SARS-associated coronavirus]

3. In the study [Synthesized peptide inhibitors of HIV-1 gp41-dependent membrane fusion. Curr Pharm Des 390 19: 1800-9] peptides derived from the HR1 and HR2 sequences of the class I viral fusion proteins have been demonstrated to possess antiviral activity through binding to the prehairpin intermediate thus blocking the formation of viral 6-HB core.

4. Cholesterylated peptide exhibits greatly increased α-helical stability and target-binding affinity [Design of 1 potent membrane fusion inhibitors against SARS-CoV-2, an emerging coronavirus with high fusogenic activity]

5. Successful peptide inhibitors of virus penetration into the host cell have been successfully developed in the case of HIV-1, Ebola virus, paramyxoviruses (SV5), respiratory syncytial virus (RSV). So, the Ebola virus was 99% inhibited when using the HIV peptide C-peptide conjugate as an inhibitor. The sequence found is characterized by the highest activity against the Ebola virus [Inhibition of Ebola Virus Entry by a C-peptide Targeted to Endosomes]

6. Inhibitor molecules included D peptides, synthetic peptides from the N and C ends of a protein virus molecule that could bind the HR1 viral domain and effectively inhibit viral infection.

In this paper, we propose a stepwise increase in the affinity of a natural peptide for a target viral protein. we have developed a phased, five-point method for determining the most suitable modified peptide. The method also includes a phased selection of the alpha-helical region for such modifications that lead to an increase in the stability of the dimer complex compared to the wild-type protein dimer, selection criteria are presented and described.

The structure of the Spike-glycoprotein
Three-dimensional structure of the dimeric complex of the peptide "blue" Spike-glycoprotein and the "green" protein Spike-glycoprotein. We will replace amino acid residues in the "blue" peptide. Interacting sites are represented by alpha-helical sites.
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Fig.1. Three-dimensional structure of the dimeric complex of the peptide "blue" Spike-glycoprotein and the "green" protein Spike-glycoprotein. We will replace amino acid residues in the "blue" peptide. Interacting sites are represented by alpha-helical sites.
_________________Coronavirus entry into host cells is mediated by the transmembrane spike (S) glycoprotein that forms homotrimers protruding from the viral surface [1]. (S) glycoprotein comprises two functional subunits responsible for binding to the host cell receptor (S1 subunit) and fusion of the viral and cellular membranes (S2 subunit). For many CoVs, (S) glycoprotein is cleaved at the boundary between the S1 and S2 subunits, which remain non-covalently bound in the prefusion conformation [2]

Let us consider in more detail the key factor determining the specificity of the host cell. The trimeric S-glycoprotein (Spike glycoprotein) localized in the envelope can be further cleaved by host cell proteases at the N-terminus, forming the S1 subunit and the membrane-bound C-terminal region, S2 subunit. Moreover, S1 contains a receptor binding domain (RBD), which directly binds to the peptidase domain (PD) of angiotensin-converting enzyme 2 (ACE2 Angiotensin-converting enzyme 2), while S2 is responsible for membrane fusion. When S1 binds to the ACE2 host receptor, another S2 cleavage site is opened and cleaved by the protease host, a process that is critical for viral infection [3]. S-glycoprotein remains non-covalent bound in a metastable conformation before fusion. After endocytosis of the virus by the host cell, a second cleavage is formed, which is mediated by endolysosomal, which allows membrane fusion activation to occur. Subunit S2 contains heptadic repeat (HR) regions: HR1 and HR2. The S1 subunit binds the cell receptor through its receptor binding domain, followed by conformational changes in the S2 subunit.
___________Protein SARS-Cov is crucial in the process of penetration of the virus into the host cell and is a promising target for the prevention and treatment of infectious diseases caused by coronovirus. The protein is folded into a spiral structure (see Fig. 2), which can be assembled into a trimeric bundle with six helices (trimer of HR1 / HR2 heterodimers).
1.Structural Basis for Human Coronavirus Attachment to Sialic Acid Receptors
2. Belouzard et al., 2009, Bosch et al., 2003, Burkard et al., 2014, Kirchdoerfer et al., 2016, Millet and Whittaker, 2014, Millet and Whittaker, 2015, Park et al., 2016, Walls et al., 2016a] [Structure, Function, and Antigenicity of the SARS-CoV-2 Spike Glycoprotein
3.Structural basis for the recognition of SARS-CoV-2 by full-length human ACE2
Three-dimensional map of the potential energy of the electrostatic interaction of the dimer complex in the regionfrom 991 amino acid residues till 1014 amino acid residues of the "blue" peptide and from 991 a.a. till 1020 a.a. of Spike-glycoprotein. Blue color indicates hydrophobic interactions, red color indicates interactions of charged amino acid residues, green color indicates interactions of hydrophilic amino acid residues. In the central part, we see a cluster of hydrophobic interactions with higher energy values.
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Fig.2. Three-dimensional map of the potential energy
Method of selection of inhibitors to the active center of the Spike-glycoprotein protein.
In this section, we will describe in detail the step-by-step instructions for determining key amino acid residues in the interaction of two proteins, methods for increasing the affinity of a protein dimer by modifying the polypeptide chain of one of the proteins, see Fig. 3 (schemas)
To maximize compliance with the secondary structure, we will investigate alpha-helical regions. The analyzed quantities in this case are log (cond (w)) and ∆H.
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Fig.3. Scheme of stepwise selection and modification of a natural peptide to increase the affinity of the dimeric complex
Step1
Description
Selection of three-dimensional structures of target proteins (dimers / tetramers). We focused on the data obtained using X-ray diffraction analysis of the Spike-glicoproteins trimeric complex (PDB: 5x5b). We opted for alpha-helical structures, which may contain interacting amino acid residues of two proteins.
Step2
Description
Control and verification of the received data can be carried out in two ways:
-to perform a calculation for two different three-dimensional structures of the same biological complex,
- perform a random experimental check, or use the previously available experimental data on the effect of substitutions of amino acid residues on affinity of binding
Step3
Description
Mutagenesis of amino acid residues of one of the alpha-helical structures of the Spike-glycoprotein protein
3.1. Calculation of the potential energy of pairwise interaction of all amino acid residues of one protein with amino acid residues of another protein for wild-type proteins. The formation of the obtained values in the form of a matrix.
3.2. Calculation of the potential energy of pairwise interaction of the dimeric protein complex, taking into account each replacement of the amino acid residue in one of the participant's polypeptide chains. The formation of the obtained energy values in the form of a matrix.
3.3. Determination of lg (cond (W)) for the interaction matrix of wild-type proteins and mutant forms of proteins.
3.4. Determination of ΔH during the transition of the system and from the interaction of mutant forms of the protein to the interaction of wild-type proteins.
3.5. Comparison of the obtained data log (cond (W)) and ∆Н in the form of graphs.
3.6. Analysis of the obtained data: the smallest value of lg (cond (W)) and the corresponding negative ∆Н.
Step4
Description
The determination of key amino acid residues, the replacement of which leads to an increase in the stability of the dimeric complex, often, these amino acid residues correspond to high potential energies of pairwise electrostatic interaction between the amino acid residues of the two proteins. We think that the surrounding values of the interaction energies of neighboring residues play an important role here. We get a set of key amino acid residues, according to the implementation of paragraph 3.6.
Step5
Description
We replace several identified amino acid residues at the same time, compare the minimum values of lg (cond (W)) and the negative values of ∆H, repeat all the steps from Step 3, but only for several substitutions at the same time: finding the potential energy of pairwise interaction, forming a matrix, calculating lg ( cond (w)) and ΔН
At the end of the calculations, we select those replacements / modifications that meet two verification criteria: the minimum values of lg (cond (W)) and the maximum negative values of ∆H. We will talk about the third criterion in more detail in the discussion section of the results.
Fig.4. A clear diagram of the analysis of changes in the potential interaction energy when replacing C1014M. Amino acid sequence of the "blue" Spike-glycoprotein a), three-dimensional structure of two interacting alpha-helical sections of the dimer b), graph of fluctuations in the potential energy of pairwise electrostatic interaction when replacing C1014M c), three-dimensional representation of the potential energy of electrostatic pairwise interaction of two truncated wild-type proteins with indication of some numerical values of the interaction d), three-dimensional representation of the potential energy of electrostatic pairwise interaction of two truncated proteins, the C1014M was replaced in the "blue" peptide, some numerical values are indicated by arrows energy e)
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Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, or 2019-nCoV) is an enveloped non-segmented positive-sense RNA virus
Two quantities lg (cond (W)) and ∆H help us estimate this change. Moreover, if the value of lg (cond (W)) decreases after replacing the amino acid residue, this may signal an increase in the stability of the dimer complex.
4We replace C1014M in the "blue" Spike-glycoprotein peptide when interacting with the "yellow" Spike-glycoprotein, the results are shown in Fig. 4. When replacing hydrophilic cysteine with hydrophobic methionine, we see significant changes in the potential energy values, in particular, a decrease in the interaction energy of methionine with other amino acid residues of the second protein.
Fig. 6c shows a comparative graph of the change in the potential energy of interaction between C1014 and M1014 with other amino acid residues of the second protein. A three-dimensional representation of such a change is shown in Fig. 4d) and 4e). The significance of such a significant change in the potential interaction energy when replacing cysteine with methionine must be analyzed, taking into account the values of the energy interactions of neighboring amino acid residues.
Two quantities lg (cond (W)) and ∆H help us estimate this change. Moreover, if the value of lg (cond (W)) decreases after replacing the amino acid residue, this may signal an increase in the stability of the dimer complex, but for a more accurate estimate, this parameter must be correlated with a change in the differential entropy ΔН. If the second value is characterized by a negative value, then this indicates the transition of the biological system to a more ordered form than with the interaction of wild-type proteins.
Fig.5.Schedule of amino acid residue substitutions in the "blue" Spike-glycoprotein interacting with the Spike-glycoprotein. The calculation was performed for the structure shown in Fig.1

The results of the numerical calculations presented on the graph allow us to conclude that some substitutions of amino acid residues starting from 994 a.a. to 1014 a.a. can significantly affect the change in the affinity of the dimeric complex. However, we do not claim that substitutions of amino acid residues up to 994 will not lead to a change in affinity.
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Fig.6. Dependence of lg (cond (W)) on the successive replacement of the amino acid residue in the "blue" peptide with MET (M), CYS (C), PHE (F), VAL (V), SER (S) during the formation of the dimeric complex (Fig 4b)

Since we are only interested in those modifications that can increase the stability of the dimeric complex, we dwell in more detail on the selection criteria:
1. The minimum value of lg (cond (W))
2. The corresponding negative value of the measure of change in differential entropy ∆Н
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Fig.7. The results of numerical calculations of changes in the differential entropy measure during the transition of a system from a modified state to a state of interaction of wild-type proteins. In the corner of each graph, the number of the replaced amino acid residue in the blue Spike-glycoprotein peptide is additionally indicated. Each of the presented amino acid residues was alternately replaced by MET (M), CYS(C), VAL (V), SER (S).

991
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19
Graph of changes in two physical quantities lg(cond(W)) and (delta)H when replacing 991T in a "blue" peptide upon binding to a viral protein Spike-glycoprotein
The results of numerical calculations demonstrate insignificant negative values (deltas)H, which is an insufficient factor for increasing the affinity of the dimeric complex. Substitution with cysteine (CYS) demonstrates a decrease in the stability and affinity of the dimeric complex.
Fig.8.

992
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandesars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19x covid19
Graph of changes in two physical quantities lg(cond(W)) and (delta)H when replacing 992Q in a "blue" peptide upon binding to a viral protein Spike-glycoprotein
The results of numerical calculations demonstrate significant negative values (deltas)H when replaced with methionine, valine and serine, which is a sufficient factor to increase the affinity of the dimeric complex. The smallest value of the physical quantity lg(cond(W)) is observed when changing to valine and serine. Substitution with cysteine demonstrates a decrease in the stability and affinity of the dimeric complex
Fig.9.

993
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19
Graph of changes in two physical quantities lg(cond(W)) and (delta)H when replacing 993Q in a "blue" peptide upon binding to a viral protein Spike-glycoprotein
The results of numerical calculations demonstrate significant negative values (deltas)H when replaced with methionine and valine, which is a sufficient factor to increase the affinity of the dimeric complex. The smallest value of the physical quantity lg(cond(W)) is observed when changing to methionine and serine. Substitution with cysteine demonstrates a decrease in the stability and affinity of the dimeric complex
Fig.10.

994
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19
Graph of changes in two physical quantities lg(cond(W)) and (delta)H when replacing 994L in a "blue" peptide upon binding to a viral protein Spike-glycoprotein
The results of numerical calculations demonstrate insignificant negative values (deltas)H, which is an insufficient factor for increasing the affinity of the dimeric complex. Substitution with cysteine (CYS) demonstrates a decrease in the stability and affinity of the dimeric complex. None of the results meet the criteria listed.
Fig.11.

995
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19
Graph of changes in two physical quantities lg(cond(W)) and (delta)H when replacing 995I in a "blue" peptide upon binding to a viral protein Spike-glycoprotein
The results of numerical calculations demonstrate significant negative values (deltas)H when replaced with methionine and serine, which is a sufficient factor to increase the affinity of the dimeric complex. The smallest value of the physical quantity lg(cond(W)) is observed when changing to methionine and serine. Substitution with cysteine demonstrates a decrease in the stability and affinity of the dimeric complex
Fig.12.

Population-based serosurveys measuring anti-severe acute respiratory syndrome coronavirus 2 (anti-SARS-CoV-2) antibodies provide. IgM and IgG antibodies to SARS-CoV-2 are generally detectable in blood several days after initial infection, although the duration of time antibodies are present. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, or 2019-nCoV) is an enveloped non-segmented positive-sense RNA virus/ Qualitative detection of IgG antibodies to SARS-CoV-2, the virus that causes COVID-19, to help identify individuals

996
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19
Graph of changes in two physical quantities lg(cond(W)) and (delta)H when replacing 996R in a "blue" peptide upon binding to a viral protein Spike-glycoprotein
The results of numerical calculations demonstrate significant negative values (deltas)H when replaced with met and phe, which is a sufficient factor to increase the affinity of the dimeric complex. The smallest value of the physical quantity lg(cond(W)) is observed when changing to methionine and serine. Substitution with cysteine demonstrates a decrease in the stability and affinity of the dimeric complex
Fig.13.
Population-based serosurveys measuring anti-severe acute respiratory syndrome coronavirus 2 (anti-SARS-CoV-2) antibodies provide. IgM and IgG antibodies to SARS-CoV-2 are generally detectable in blood several days after initial infection, although the duration of time antibodies are present. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, or 2019-nCoV) is an enveloped non-segmented positive-sense RNA virus/ Qualitative detection of IgG antibodies to SARS-CoV-2, the virus that causes COVID-19, to help identify individuals

997
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19
Graph of changes in two physical quantities lg(cond(W)) and (delta)H when replacing 997A in a "blue" peptide upon binding to a viral protein Spike-glycoprotein
The results of numerical calculations demonstrate significant negative values (deltas)H when replaced with methionine and valine, which is a sufficient factor to increase the affinity of the dimeric complex. The smallest value of the physical quantity lg(cond(W)) is observed when changing to methionine and serine. Substitution with cysteine demonstrates a decrease in the stability and affinity of the dimeric complex
Fig.14.

998
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19
Graph of changes in two physical quantities lg(cond(W)) and (delta)H when replacing 998A in a "blue" peptide upon binding to a viral protein Spike-glycoprotein
The results of numerical calculations demonstrate significant negative values (deltas)H when replaced with methionine and serine, which is a sufficient factor to increase the affinity of the dimeric complex. The smallest value of the physical quantity lg(cond(W)) is observed when changing to methionine, phe and serine. Substitution with cysteine demonstrates a decrease in the stability and affinity of the dimeric complex.
Fig.15.

999
Population-based serosurveys measuring anti-severe acute respiratory syndrome coronavirus 2 (anti-SARS-CoV-2) antibodies provide. IgM and IgG antibodies to SARS-CoV-2 are generally detectable in blood several days after initial infection, although the duration of time antibodies are present. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, or 2019-nCoV) is an enveloped non-segmented positive-sense RNA virus/ Qualitative detection of IgG antibodies to SARS-CoV-2, the virus that causes COVID-19, to help identify individuals
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19
Graph of changes in two physical quantities lg(cond(W)) and (delta)H when replacing 999E in a "blue" peptide upon binding to a viral protein Spike-glycoprotein
None of the results meet the criteria listed.
Fig.16.

1000
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19
Graph of changes in two physical quantities lg(cond(W)) and (delta)H when replacing 1000I in a "blue" peptide upon binding to a viral protein Spike-glycoprotein
The results of numerical calculations demonstrate significant negative values (deltas)H when replaced with methionine and serine, which is a sufficient factor to increase the affinity of the dimeric complex. The smallest value of the physical quantity lg(cond(W)) is observed when changing to phe and serine. Substitution with cysteine demonstrates a decrease in the stability and affinity of the dimeric complex
Fig.17.
Population-based serosurveys measuring anti-severe acute respiratory syndrome coronavirus 2 (anti-SARS-CoV-2) antibodies provide. IgM and IgG antibodies to SARS-CoV-2 are generally detectable in blood several days after initial infection, although the duration of time antibodies are present. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, or 2019-nCoV) is an enveloped non-segmented positive-sense RNA virus/ Qualitative detection of IgG antibodies to SARS-CoVsars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19-2, the virus that causes COVID-19, to help identify individuals

1001
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19
Graph of changes in two physical quantities lg(cond(W)) and (delta)H when replacing 1001R in a "blue" peptide upon binding to a viral protein Spike-glycoprotein
The results of numerical calculations demonstrate significant negative values (deltas)H when replaced with methionine and serine, which is a sufficient factor to increase the affinity of the dimeric complex. The smallest value of the physical quantity lg(cond(W)) is observed when changing to valine and serine. Substitution with cysteine demonstrates a decrease in the stability and affinity of the dimeric complex.
Fig.18.
Fig.19. The results of numerical calculations of substitutions of amino acid residues from 1011a.a. to 1014 a.a. alternately with MET (M), CYS (C), PHE (F), VAL (V), Ser (S).
As can be seen from the graphs in Fig. , each replacement of the amino acid residue with cysteine leads to a decrease in the stability of the dimeric complex and to an increase in the measure of change in differential entropy. Thus, we do not recommend the use of cysteine substitutions of these amino acid residues to increase the affinity of the dimeric complex.
sars cov 2, sars, sars cov, pfizer vaccine, pfizer covid vaccine, pitch deck, pharmacology made easy,
sars cov 2, sars, sars cov, parabolic sar, sars cov igm, covid19, covid19 gov, covid19 gov tr, covid19 saglik gov tr,yandex covid19
Population-based serosurveys measuring anti-severe acute respiratory syndrome coronavirus 2 (anti-SARS-CoV-2) antibodies provide. IgM and IgG antibodies to SARS-CoV-2 are generally detectable in blood several days after initial infection, although the duration of time antibodies are present. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, or 2019-nCoV) is an enveloped non-segmented positive-sense RNA virus/ Qualitative detection of IgG antibodies to SARS-CoV-2, the virus that causes COVID-19, to help identify individuals
Fig.20. The results of numerical calculations of the change in the measure of differential entropy (delta)H when alternately replacing the amino acid residues from 1011 a.a. to 1014 a.a. with MET (M), CYS (C), PHE (F), VAL (V), SER (S).

Any replacement of PHE1013 with MET (M), CYS (C), PHE (F), VAL (V), SER (S) leads to an increase in the measure of differential entropy, so we also do not recommend these substitutions to increase the affinity of the dimer complex . The most significant result was obtained with the replacement of 1014 a.a. on MET (M), PHE (F), VAL (V), SER (S), since all the obtained ∆H values are in the negative range of values, the value log (cond (W)) is also characterized by values in a lower range of values .
sars cov 2, sars, sars cov, pfizer vaccine, pfizer covid vaccine, pitch deck, pharmacology made easy,
Population-based serosurveys measuring anti-severe acute respiratory syndrome coronavirus 2 (anti-SARS-CoV-2) antibodies provide. IgM and IgG antibodies to SARS-CoV-2 are generally detectable in blood several days after initial infection, although the duration of time antibodies are present. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, or 2019-nCoV) is an enveloped non-segmented positive-sense RNA virus/ Qualitative detection of IgG antibodies to SARS-CoV-2, the virus that causes COVID-19, to help identify individuals
The fifth final stage
At the fifth final stage, we have to select the amino acid residues in the wild-type peptide of the blue Spike-glycoprotein, which we will modify. In this work, the primary task was to disclose the methodology for the stepwise selection and modification of peptides to increase affinity for the second protein. The finding of a high affinity peptide is shown here as an example on several amino acid residues. In order to find all possible modifications of the peptide, it will be necessary to carry out a similarly extensive numerical study, which is beyond the scope of this work.
We took 4 amino acid residues: 997, 998, 1002 and 1006, made replacements for them with Met, GLN, ASN, obtained potential energy matrices, calculated the values of Lg (cond (W)) and ∆H. The results of the calculations are shown in Fig. 21
Population-based serosurveys measuring anti-severe acute respiratory syndrome coronavirus 2 (anti-SARS-CoV-2) antibodies provide. IgM and IgG antibodies to SARS-CoV-2 are generally detectable in blood several days after initial infection, although the duration of time antibodies are present. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, or 2019-nCoV) is an enveloped non-segmented positive-sense RNA virus/ Qualitative detection of IgG antibodies to SARS-CoV-2, the virus that causes COVID-19, to help identify individuals
Fig.21. A graphical representation of the numerical results of numerical modeling of several simultaneous modifications of amino acid residues in the blue Spike-glycoprotein at 997, 998, 1002, 1006, 1008 amino acid residues. Substitutions were made with MET, GLN, ASN.
Change in lg (cond (W)) a), change in ∆Н b).

Thus, the conclusions drawn from numerical calculations on the modification of the natural peptide allow us to conclude that the simultaneous replacement of amino acid residues 997MET and 1002MET can lead to an increase in the affinity of the dimeric complex formed by the modified natural viral peptide and the Spike-glycoprotein protein. Since the affinity of such a modified complex may exceed the interaction of wild-type viurs proteins, this method will allow finding inhibitors by the competitive type of binding
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antibodies against SARS-CoV -2, the virus which causes the disease COVID-19 in general, a positive antibody test is presumed to mean a person has been infected with SARS-CoV-2, the virus that causes COVID-19 Roche Diagnostics has developed a serology test for detecting antibodies to the severe acute respiratory syndrome coronavirus 2 that causes COVID-19 Studies from serum samples could transform our understanding of the spread of COVID-19, but what antibodies alone say about immunity Antibody responses against enveloped viruses, such as SARSCoV2, are usually comprised of immunoglobulin (Ig) M, IgG3, IgG1 and IgA COVID-19 is an infectious disease caused by the SARS-CoV-2 virus that spreads easily between people in a similar way to the common
Discussions and conclusions.
_______This article described a method for phasing the affinity of a natural peptide to a target viral protein by modifying the peptide. The selection criteria for the most suitable modifications were given, among which the following can be listed: the stability of the dimer complex by calculating the value of log (cond (W)) and comparing the obtained value with the value of log (Cond (W)) obtained for the wild-type dimer and other modified dimers .
_______The next indicator was the measure of the change in differential entropy ∆Н, which characterizes the ordering of the system. Moreover, the values of lg (cond (W)) and ∆Н are interrelated: the minimum number lg (cond (W)) must correspond to a negative value of ∆Н, otherwise, the dimeric complex does not satisfy the necessary criteria.
________As an example of the selection of suitable modifications of natural peptides, the Spike-glycoprotein viral protein was selected, which is responsible for the attachment of the virus to the cell and the incorporation of the viral genome into the cell. In this work, we analyzed the Central helix region of this protein, performed mutagenesis, and calculated the stability of the formed dimeric complexes upon modification of the natural peptide in the region of the Central helix region. The calculation results showed that the modification of the site from 995 a.a. till 1014 a.a. most likely to affect the affinity of the modified peptide for the Spike-glycoprotein viral protein. In the course of the numerical simulation, wild-type peptide mutagenesis was performed, the calculation of the values of log (cond (W)) and ΔH, the minimum values of log (cond (W)) were compared with negative values of ΔH, since these values are analyzed in pairs. If the log (cond (W)) values take the minimum values, and the ΔH value is in the range of positive values, then this modified peptide does not pass the test according to the criteria.
________To reduce false results, we remove from further analysis all dimeric complexes that are characterized by a ∆H value in the positive range of values. We also believe that an important aspect affecting the results of the modification of a natural peptide is the environment of the modified portion of the polypeptide chain with other amino acid residues, the location of which in turn depends on the solvent (water, impurities, salts, temperature, pH). in three-dimensional space is characterized by the distribution of potential energy of interaction with other amino acid residues in three-dimensional space. Replacing even one amino acid residue in a polypeptide chain can serve as a substantial redistribution of the potential energy of interaction with all amino acid residues of the adjacent polypeptide chain, which in turn will affect the stability of the dimer complex and the entropy of the dimer complex, and more precisely, entail measures to change the differential entropy of the dimer complex ∆H , which we calculate for each replacement.
______By analyzing the Spike-glycoprotein protein peptide in this way, we determined amino acid residues, the replacement of which can affect the affinity, namely, the increase in affinity due to increased stability of the dimeric complex and ordering of the system of two proteins. The aim of this work was to develop and describe in detail a methodology for increasing the affinity of a natural peptide for a target protein by modifying the peptide, namely, replacing amino acid residues. In the course of the work done, several key amino acid residues found were replaced with 997, 998, 1002, 1006, 1008, see fig. on MET (M), GLN (), ASN ().
________The results presented in fig. and in the table it was possible to determine the most suitable modification of the peptide to increase the affinity of interaction with the Spike-glycoprotein viral protein. These modifications are two substitutions ALA997MET and ALA1002 MET, since two simultaneous substitutions significantly reduced the value of log (cond (W)), and the value of ∆Н was characterized by the lowest negative value. A good result was also obtained with the simultaneous replacement of two amino acid residues in the peptide ALA997MET and ALA1002GLN, as well as ALA997MET and ALA1008MET. The worst result was obtained with the simultaneous replacement of ALA998MET and LEU1006GLN, since the value of log (cond (W)) was obtained in a high range of values, and the value of ΔН was in the range of positive values.
To identify a high affinity modified peptide for the wild-type virus virus Spike-glycoprotein, it is necessary to perform large-scale numerical calculations and, based on the results, obtain the most suitable modifications of the peptide for further refinement by increasing the resistance of peptides against protease cleavage and increasing the circulation time in the body to achieve a significant therapeutic effect .
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Three-dimensional map of the energy interaction of the amino acid sequences of an antibody with an antigen
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Population-based serosurveys measuring anti-severe acute respiratory syndrome coronavirus 2 (anti-SARS-CoV-2) antibodies provide. IgM and IgG antibodies to SARS-CoV-2 are generally detectable in blood several days after initial infection, although the duration of time antibodies are present. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, or 2019-nCoV) is an enveloped non-segmented positive-sense RNA virus/ Qualitative detection of IgG antibodies to SARS-CoV-2, the virus that causes COVID-19, to help identify individuals

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Population-based serosurveys measuring anti-severe acute respiratory syndrome coronavirus 2 (anti-SARS-CoV-2) antibodies provide. IgM and IgG antibodies to SARS-CoV-2 are generally detectable in blood several days after initial infection, although the duration of time antibodies are present. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, or 2019-nCoV) is an enveloped non-segmented positive-sense RNA virus/ Qualitative detection of IgG antibodies to SARS-CoV-2, the virus that causes COVID-19, to help identify individuals
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