# Skin math: growing the epidermis based on mathematical modeling

The human body can be safely compared with a very complex and sometimes confusing mechanism, to which no instruction was attached, therefore scientists have to figure it out for themselves. There are many systems in our body, from nervous to immune, each of which performs its own specific functions and communicates with other systems, which allows the body to function effectively. In the research community, the lion's share of attention goes to the nervous system. Everyone pulls to reveal the secrets of our brain, which is so often compared by mystery with the Universe. But other systems are no less interesting, complex and important. Today we will look at a study that combines mathematics, biochemistry and a lot of curiosity. And the purpose of this study is the epidermis, I mean human skin. How did mathematics help scientists understand what they lacked in the process of growing their skin and what did they get as a result? We will try to answer these and other questions with the help of a research group report. Go.

Human skin is not as simple as it might seem at first glance. Someone may consider it just a shell, and some may be considered a “bag for bones.” But let us leave aside the statements of the most immoral robot in the world named Bender and dive into the structure of human skin.

First, the skin is the largest organ of the human body (other creatures will not be affected, given the study in question), consisting of three main subsystems: the epidermis (outer layer), the dermis (connective tissue between the upper layer of the skin and organs) and subcutaneous fat cellulose (thermostatic and protective layer with the function of "storage" of nutrients).

The structure of human skin.

Since in the study, scientists "conjure" over the epidermis, we consider this layer in more detail.

The epidermis of a person, if you equally love anatomy and cooking, resembles the cake Napoleon, for it consists of five layers. In each of the layers, there are cells that are the main “subjects” in the study under consideration - keratinocytes. In the epidermis, they generally occupy the lion's share - about 90% of all cells.

Functions of keratinocytes vary depending on the belonging to a particular layer:

• basal - the closest layer to the dermis, in which such cells as keratinocytes are called basal, which is quite logical. These cells, in conjunction with stem cells, are involved in an important process - regeneration of the epidermis. Also in the cytoplasm of keratinocytes there are melanosomes - melanin granules, obtained from melanocytes (cells), which protect us from exposure to ultraviolet radiation.
• prickly layer got its prickly name due to the unusual structure of keratinocyte cells that have spiky processes for connecting with each other. In the cytoplasm of local keratinocytes, keratin is synthesized, which is involved in the formation of hair and nails. From a biological point of view, keratin is inferior in physical strength only to chitin. In addition, there are keratinosomes that make our skin hydrophobic.
• granular layer - keratinocytes also possess keratinosomes, i.e. they prevent dehydration of the skin. Also, keratinocytes in this layer synthesize some proteins.
• the brilliant layer is named so, since microscopy does not reveal cells, and the layer itself looks like a uniform strip of pink. So it is - the nuclei, organelles and the intercellular compounds of keratinocytes in this layer are destroyed. At the same time there is a substance that binds keratinocytes (or what remains of them). It makes the skin firm.
• horny - the outer layer of the epidermis in contact with the environment. And it can also be called the most real cellular cemetery, because it is formed from dead keratinocytes (called horny scales), which are constantly updated. This provides effective protection against external factors.

Cell keratinocyte

It is also worth mentioning the fact that keratinocytes are involved in wound healing. When the skin is damaged, keratinocyte cells begin to actively divide and migrate to the area of ​​injury where epithelization occurs, that is, the wound begins to grow.

As we can understand from these layers, there is a lot of keratinocytes and they perform different functions when they work together with cells of a different type. Universal soldiers among the cells of the epidermis, nothing else.

What is the problem of research, you ask? And the fact that the normal layer of the human epidermis is about 100 microns thick, but the artificial (created by passaging keratinocytes) is only 10 microns.
Пассирование клеток* — отбор необходимого числа клеток для их дальнейшего выращивания на субстрате (например, в чашке Петри).
Such an epidermis will simply be ineffective, like a papier-mâché tank. And here can help mathematics, namely the mathematical model. About her and talk further.

The basis of the research

Scientists have previously used mathematical models as the basis of the process of creating human epidermis. In this study, a new method of epidermal homeostasis was developed, which is based on a mathematical model of keratinocytes derived from stem cells distributed in the basal layer. It should be noted that the model also took into account dynamic processes in the epidermis (migration and differentiation of skin cells) and intracellular processes associated with Ca 2+ .

This mathematical model made it possible to understand that the most important role in the synthesis of the epidermis of the required thickness and structure is played by the distribution of stem cells and the structure of the basal membranes separating the connective tissue from the epithelium.

If we speak more specifically about such an indicator as thickness, then it is the basal membranes that play the main role. To achieve the desired result, scientists applied a sinusoidal modulation to the shape of the basement membrane, changing the amplitude and wavelength. As a result, it was found that a stable structure of the epidermis of the required thickness requires a wavy basement membrane with a large amplitude and short wavelength. That is, the waviness of the papillary layer located above the dermis and under the epidermis is crucial for creating a model of the epidermis that is close to real physiological parameters.

In addition to the thickness and strength of human skin also has hydrophobicity, which depends on the thickness of the stratum corneum. Accordingly, the thickness of this layer should also be taken into account in the experimental model for a more realistic reconstruction of the epidermis.

Combining all the desired and necessary, scientists have designed a model to demonstrate the possibility of creating an approximate to the reality of the epidermis, which includes the stratum corneum and the intercellular lamellar lipid structure. Realization of all this was carried out by seeding passaged keratinocytes on the wavy surface of the polyester base in open Petri dishes.

The results were very successful, which confirmed not only the usefulness and correctness of this growing method, but also the importance of using mathematical models as a tool for predicting processes.

Results of the study

Image No. 1

The images above show the simulation results and the results of growing the epidermis based on this simulation.

Researchers draw our attention to two very significant images ( 1A and 1B ). In the first case there is a flat basement membrane, in the second - a sinusoidal membrane, which allowed increasing the thickness and strength of the epidermis.

But this is only a model, albeit with very attractive results, for which it is necessary to establish what parameters should be the basis for sowing (polyester). For this, the structure of the papillary layer, whose thickness in humans is 51 microns, and the waviness interval - 105 microns was analyzed (the skin on the abdominal cavity was analyzed, the average age of the study participants was 36.3 years).

The image 1C shows images (color obtained by hematoxylin and eosin) of the resulting epidermis with different variants of the base (# 200, # 255, # 300, # 350, # 460 and # 480). At the very top of the image (“ Control ”) - the epidermis without a wavy base acts as a control group for comparing the results.

The most interesting for scientists were options # 200, # 255 and # 300, which showed a good thickness in comparison with the control sample. The live layer of the epidermis based on # 255 was thicker than that based on # 200 and # 300. Therefore, this option was chosen for further study.

A short conclusion - the wave-like basis for seeding leads to an increase in the number of living cells of the epidermis and to its thickening and compaction, which brings the grown sample to the real human epidermis.

Image No. 2

Structural proteins filaggrin, loricrin, claudine 1 and ZO-1 play a key role in the epidermis. In order to check whether the expression (synthesis) of these proteins proceeded normally, the scientists conducted an immunohistochemical study of the epidermis grown on the # 255 base.

Filaggrin ( 2A), loricrin ( 2B ) and ZO-1 ( 2C ) were expressed in the upper layer of the epidermis. And expression of claudine 1 was carried out in the cell membrane along the entire plane of the epidermis ( 2D ).

Pay attention to the image of 2G, on which a certain layer is marked with a black arrow and a “*” sign - horny. This suggests that this synthesized epidermis has good protective (against external factors) characteristics.

An immunohistochemical study was also conducted with the epidermis on the basis of # 300, in order to compare with the parameters of the epidermis # 255. The expression of claudine 1 and ZO-1 was detected in both variants, but at # 255 it was significantly stronger. In confirmation of this, another test was performed - measurement of transepidermal water loss of the control and # 255 samples. The graph of the results of this test ( 2H ) clearly demonstrates that the water loss of sample # 255 is much lower, which once again confirms its high barrier (and protective) characteristics.

Image No. 3

Sample staining with anti-bromodeoxyuridine antibodies (anti-BrdU) showed that proliferating cells are present only in the lower part of the control sample ( 3A), while in the test sample # 255 the same cells were found on the fibers of the polyester base ( 3B , black arrows).

The researchers also tested the CSPG4 protein, which plays a very important role in the interaction of the cell and substrate. The analysis showed the presence of these cells on the base fibers ( 3D , white arrows), which indicates the presence of cells on the fibers, some of which have proliferating properties.

In addition, testing was conducted with anti-bromodeoxyuridine antibodies and K14, which is a marker of the basal layer of the epidermis. Sample # 255 showed a unique result - the presence of K14 and BrdU on the surface of the polyester base. This suggests that proliferating cells recognize the surface of the base as the basal layer.

The next subject was YAP protein, which is involved in the regulation of transcription (RNA synthesis in cells by DNA). In the control sample, YAP was located exclusively on the basal layer ( 3E ). But in the test sample, YAP was present around the fibers ( 3F , red arrows).

The use of small interfering RNAs in the process of analyzing the activity of the YAP protein led to the destabilization of the three-dimensional structure ( 3G and 3H ).

In the control sample using small interfering RNA, YAP protein was expressed around the fibers ( 3I ), and in the test sample the expression was insignificant ( 3J). But despite this, the use of small interfering RNA had no effect on the proliferation of keratinocytes.

For a more detailed acquaintance with the nuances and details of the study, I strongly recommend that you look into the report of the research group and additional materials to it.

Epilogue

This study combines biochemistry and mathematics. Of course, these two sciences very often go together, if scientists intend to get reliable and adequate results. The use of mathematical modeling in this case helped to understand the importance of the wave-like basis for growing the epidermis, which significantly increases the number of living cells and, as a result, the thickness and strength of the sample.

This work was mostly aimed at testing the operability of the mathematical model, and not the epidermis cultivation technique itself. The difficulties that researchers faced earlier will no longer prevent them from continuing to study in more detail the methods of cell synthesis and growing the epidermis in a form that will be as close to real as possible.

The results of this work may well be a rather important step forward both for transplantology and for the study of human skin in general, as well as to push other researchers to more actively use mathematical modeling as a tool of primary importance.

Thank you for your attention, stay curious and have a great work week guys.

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