Pharmacy and Drug Development

Abstract

Purpose. Identifying the results of the application in silico of the basic structures, in the study of the endothelial proprotective properties of drugs for the treatment of coronavirus infection (COVID-19), affecting the pharmacological targets of the cardiovascular system (CVS). 

The article is aimed at researchers in the field of theoretical and experimental pharmacology and medicine. 

Materials and methods. We accept the physico-mathematical model "damper-spring" as a theoretical and experimental justification for the development of methods for mathematical modeling in silico of basic structures, for studying the endothelioprotective properties of drugs.  We introduce theoretical and experimental development in silico of basic structures in the study of endothelioprotective properties of drugs for the treatment of coronavirus infection (COVID-19).

Outcomes.  Established by the experimental pathway influence of endothelial function and values of cost in silico coefficients and  

Introduction

In the past few years, it has been argued that clinical trials on the in-silico model are effective as pharmacological targets of the cardiovascular system (CCC). An in silico clinical trial is conducted as an individual computer simulation used in the development or normative evaluation of a drug, device or intervention.

This kind of model (as in silico) makes it possible to study the behavior of the system when internal characteristics and external conditions change, to create and implement scenarios, to solve the optimization problems of the aggregate system. However, in each computer implementation of the model, a specific biological identification corresponds to the constantly changing pharmacological targets of the cardiovascular system (CCC).  so-called tuning coefficients. And this, very much complicates on its turn the mathematical model. 

Up to the point of this scientific study, there are problems: - Completely simulated clinical trials in silico, the basic structures affecting pharmacological targets of the cardiovascular system (CCC) are impossible with the application of modern technologies and today's understanding of the ongoing processes in biological structures. But, after applying this new methodology of mathematical modeling of the endothelium and as a result of this study, in silico model development is expected to have significant advantages over current in vitro, ex vivo and in vivo clinical trials – and research in this area is ongoing [1].

The endothelium, together with the vascular wall of the artery and vein, is an integral (holistic) organ, capable of responding to mechanical action ("for example, cyclic stretching or fluid shift tension): flowing blood, the amount of blood pressure in the lumen of the vessel and the degree of tension of the muscular layer of the vessel" [2].

In the pharmacological study of biological objects, many models have been created for all these processes. It seems that for each study a special model is created to confirm a certain theoretical prediction. Today, at least there is no single universal model on which to conduct all pharmacological experiments!

Materials And Methods

A. Physical and mathematical model "damper-spring" [3] as a theoretical and experimental justification for the development of methods for mathematical modeling in silico of basic structures, for the study of endothelioprotective properties of drugs. 

The reaction of endotheliocytes and smooth muscle cells (MMC) vessel wall to the cardiovascular system (CCC) to mechanical and chemical influences leads us to apply the mechanical model "damper-spring" (Figure 1). 

At the right end of the flap by the model we have a spring, which is calculated by the equation according to Hooke's law:

Where: - moving the end of the B turns to the spring and - the stiffness of the spring 

Since in our case the spring is compressed, the equation takes the form:

This force is called the "blood vessel constriction force", which is right proportional to the value of the resistance of the elastic fibers (the inner elastic membrane and the outer elastic membrane of the vascular wall of the artery and vein) and is directed in the opposite direction to the pressure () of the blood vessels.

At the left end of the flap the model, of t. 0 to t.  A have distributed blood pressure forces (mechanical and chemical effects on the walls of blood vessels) and as a result, the value of tuning coefficients according to the in-silico model: (stronger than active),  (average active) and (weakly active). And corresponding values (weakly active),  (average active) and (stronger active). 

The effective force of value ,  and (,  and ) is the force that acts in t.  A flap and is directed in the opposite direction - "the force of narrowing the blood vessel".

In the specific case, the numerical values and (mechanical and chemical effects) is the collection of suma from all coefficients indicating the degree and direction of activity of the pharmacological targets of the cardiovascular system (CCC) on the functions of endotheliocytes, smooth muscle cells (MMC) and the vessel wall to deterioration or to improvement. We can write: 

For a mechanical model in the form of a "damper-spring" on a physico-biological control object (FBOU) (Figure 1), we will make a mathematical model in dynamics, with a differential equation, in the form of [3]:

Looking at equation (3) and equation (4), equation (5) takes the form:

Note: The values - with a conditionally negative effect on the functions of endotheliocytes, smooth muscle cells (MMC) and the vessel wall include both cyclic stretching and fluid (blood) shear tension.  The values include all elements with a conditionally positive effect on the functions of endotheliocytes, smooth muscle cells (MMC) and vessel walls, including both cyclic stretching and fluid (blood) shear tension. 

Thus, the cost (Figure 1) of the effective strength  depends on the potentially positive and/or negative effects of the function of endothelial cells, smooth muscle cells (MMC) and the vessel wall on the state of homeostasis and activity pharmacological targets of the cardiovascular system (CCC). A, numerical values and (mechanical and chemical effects) are included in  in silico models of basic structures for the study of endothelioprotective properties of medicines.

B. Theoretical and experimental development in silico of basic structures in the study of endothelioprotective properties of drugs for the treatment of coronavirus infection (COVID-19). 

Using the ATC (Anatomical-Therapeutic-Chemical) classification of drugs [4], we will build in silico models to study the endothelioprotective properties of drugs for the treatment of coronavirus infection (COVID-19).

Note: ATC (Anatomical-Therapeutic-Chemical) classification. Full English name - Anatomical Therapeutic Chemical Classification System (ATCCS) [4]. Taking into account the side effects, drug interactions and contraindications for experimental and literature data on conditionally antiviral drugs used to treat coronavirus infection COVID-19, we introduce coefficients c and d.

Where the coefficient c indicates: Potential negative effect of the drug substance on endothelial function, and coefficient d indicates: Potential positive effect of the drug substance on endothelial function. (Table 1)

Table 1 - Potential positive and negative effects on endothelial function (EF) of medicinal substance drugs used to treat COVID-19 coronavirus infection

Coefficient/Value	Activity	Endothelial function
Results And Discussion Looking for a transfer function of embarrassing effects (the effective force  of potentially positive and/or negative effects of endotheliocyte function, smooth muscle cells (MMC) and vessel walls on the state of homeostasis and the activity of pharmacological targets of the cardiovascular system (CVS)):   Replace   and Get:   - is a pharmacological coefficient - with a potentially negative or positive effect of pharmacological targets of the cardiovascular system (CCC).   See equation (5):  We get:   Where:   - Potential negative effect of pharmacological targets of the cardiovascular system (CVS) on the function of endotheliocytes, smooth muscle cells (MMC) and the vessel wall. – Potential positive effect of pharmacological targets of the cardiovascular system (CCC).  on the function of endotheliocytes, smooth muscle cells (MMC) and vessel walls.  It's easy to notice what makes sense when i.e., Thus, the potential negative effect of pharmacological targets of the cardiovascular system (CVS) on the functions of endotheliocytes, smooth muscle cells (MMC) and the vessel wall should not exceed half the absolute value of the potential positive effect of pharmacological targets of the cardiovascular system (CVS). Table 2 – Numerical values of pharmacological coefficients depending on  the value of in silico coefficients and as pharmacological targets of the cardiovascular system (CCC). in silico коэффициенты   и    stronger active     average active   inactive     stronger active         average active …       inactive       Applying the equations and values from the tables (Table 1) and (Table 2): Consider obtaining the results from the application in silico of the model of basic structures for the study of endothelioprotective properties of drugs used to treat coronavirus infection COVID-19 based on ATC (Anatomical-therapeutic-chemical) classification of drugs (Table 3): Table 3 - Effect of endothelial function values of the in-silico model of antiviral drugs used to treat coronavirus infection COVID-19 based on ATC (Anatomical-Therapeutic-Chemical) classification of drugs and their values.  №  by series  Name  Drug Classification: by ATC модели in silico and their meanings Influence of endothelial function 1. Hydroxychloroquine and Chloroquine  P01BA02     High degree of deterioration  2. Lopinavir  and Ritonavir J05AR10     High degree of deterioration  3. Adalimumab     Bevacizumab   Тоцилизумаб* (Атлизумаб) L04AB04 L01XC07     L04AC07               Medium degree of deterioration High degree of deterioration  Moderate deterioration 4. Corticosteroids: Methylprednisolone, combinations   Dexamethasone, combinations H02BX  H02BX01     QH02BX90               High degree of deterioration  Moderate deterioration 5. Tofacitinib   L04AA29    High degree of deterioration  6. Baricitinib L04AA37     High degree of deterioration  7.  Ruxolitinib L01XE18     Moderate deterioration 8. Interferons:   Interferon alfa-2b     Interferon beta-1 alpha L03AB    L03FROM01     L03AB02                 High degree of deterioration  High degree of deterioration 9. Remdesivir CAS:1809249-37-3     Moderate deterioration 10.  Favipiravir J05AX27   Low degree of deterioration 11.  Ribavirin J05AP01     Moderate deterioration 12. Chlorprothixen N05AF03     Moderate deterioration  13. Camostat B02AB04   Low degree of deterioration 14. Mepolizumab R03D   Low degree of deterioration 15. Convalescent plasma      Low degree of deterioration 16. Antibodies to Spike       Low degree of deterioration 17. Immunoglobulins,       Low degree of deterioration We will compile and present in tabular form the relationship between pharmacological coefficients and values in silico coefficients and,  to varying degrees of deterioration in the function of endotheliocytes, smooth muscle cells (MMC) and vessel walls, as pharmacological targets of the cardiovascular system (CCC). (Table 4) Table (4) 2 – Numerical values pharmacological coefficients and associations of the degree of deterioration in the function of endotheliocytes, smooth muscle cells (MMC) and vessel walls, as pharmacological targets of the cardiovascular system (CCC). Pharmacological coefficients                    Values   in silico coefficients and                           +                 +            +               +          +              +               +     +                 +    +              +      +                      +              +            +               +            +           +     Conclusion Let's summarize the results of the study - evaluate and experimentally determine the conditions for the implementation and directions of the way of application pharmacological coefficients   and:  The first group of drugs with an in-silico coefficient () of pharmacological activity of the drug substance to the functional state of the endothelium include: Hydroxychloroquine and Chloroquine; Lopinavir and Ritonavir; Bevacizumab, Methylprednisolone, combinations, Tofacitinib, Baricitinib, Interferon beta-1alpha and Interferon alfa-2b. Their use in clinical practice can lead to a high degree of deterioration in endothelial function - quickly lead to endothelial dysfunction (ED). The second group of drugs with an in-silico coefficient () of pharmacological activity of the drug substance to the functional state of the endothelium include: Adalimumab, Tocilizumab (Atlizumab), Dexamethasone, combinations, Ruxolitinib, Remdesivir, Ribavirin and Chlorprothixen. Their use in clinical practice can lead to an average degree of deterioration in endothelial function.  – Slowly lead to endothelial dysfunction (ED). The third group of drugs with an in-silico coefficient () of pharmacological activity of the drug substance to the functional state of the endothelium include: Favipiravir, Camostat, Mepolizumab, Convalescent plasma, Antibodies to Spike and Immunoglobulins. Their use in clinical practice can lead to a low degree of deterioration in endothelial function - practically not lead to endothelial dysfunction (ED).  Thus, the coefficients (c1, c2 and c3; d1, d2 and d3) in the application of pharmacological in silico basic structures in the study of endothelioprotective properties of drugs for the treatment of coronavirus infection (COVID-19), are active pharmacological coefficients.  Which can be taken as pharmacological coefficients in future research in fundamental pharmacology and medicine on the physico-biological objects of control of the FBOU (endotheliocytes + smooth muscle cells (MMC) and vessel walls), physico-biological systems of automatic regulation (FBSAR) and homeostasis of the cardiovascular system (CCC). References Kaniskov, Vasil Lyubenov, author 2022, Synergy of quantum mechanisms in biological structures. 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View at Publisher | View at Google Scholar Classification system of anatomical therapeutic chemicals (ATC) WHOCC – Home [electronic resource] https://www.whocc.no/ View at Publisher | View at Google Scholar Quick linksss Abstract Introduction Materials And Methods Results And Discussion Conclusion References Become an Editorial Board Member Register here Become a Reviewer Register here What our clients say Douglas Miyazaki I would like to express my gratitude towards you process of article review and submission. I found this to be very fair and expedient. Your follow up has been excellent. I have many publications in national and international journal and your process has been one of the best so far. Keep up the great work. Bahceci Selen I am very glad to say that the peer review process is very successful and fast and support from the editorial Office. Therefore I would like to continue our scientific relationship for a long time. 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