Biophysical Model of Active Transport Through Vesicles Authors Janos Vincze, Gabriella Vincze-Tiszay

Home , Active transport, Endocytosis, Pinocytosis

Janos Vincze et al. Medical Research Archives vol 8 issue 4. Medical Research Archives

RESEARCH ARTICLE

Biophysical model of active transport through vesicles Authors Janos Vincze, Gabriella Vincze-Tiszay

Affiliations Health Human International Environment Foundation, Budapest, Hungary

Abstract

The transport phenomena in the human organism mean the variation in time and space of generalized forces when they generate flows for which conservation laws apply. The more specific transport mechanisms are the following; ion pump, transporting molecules, ionic channels and active transport through vesicles. The process of cytopempsis, or the process of transport via the vesicles, is also a vesicular process, initiated in the membrane area. The vesicle in this case constitutes a means of transport of the substances through cell, the contents of the vesicle as a whole being transported through the cytoplasm, and then released. Endocytosis consists of the transport of substances from the extracellular environment to the interior of the cell with the help of a vesicle formed by the cell membrane. Exocytosis is the process by which the fusion of some vesicles of the cytoplasm with the cell membrane is produced being followed by the expulsion of the vesicle content outside the cell. The pattern of the pinocytosis considers its static character, which is the probability to form vesicles. This mathematical model is applicable from all active transport through vesicles.

Keywords: transport phenomena, pinocytosis, endocytosis, phagocitosis, mathematical model

Janos Vincze et al. Medical Research Archives vol 8 issue 4. April 2020 Page 2 of 9

Introduction conductibility, crossed effects and other); 2.) it allows a quantitative characterization of The transport phenomena in the human the product exchange, which was impossible organism mean the variation in time and based on the previous definitions. space of generalized forces when they If W – the amount of the transported generate flows for which conservation laws parameter, for which the conservation law is apply (J. Vincze 1970 [1]). valid; K – a constant dependent on the type This general and strongly scientific of transportation and the nature of the definition of the transportation phenomena transported parameter; grad a – the has two major merits: 1) particular forms of generalized force, then the amount of the transportation can be deducted from it (mass parameter (flow) transported through the transport – diffusion; energy transport – surface dS in the dt time frame will be given thermal conductibility; impulse transport – by the relation: viscosity; electric charge transport – electric

t2 grad a dS dt W = K   t1 S (x, y,z)

If the transportation takes place only after a direction x, then we obtain the formula:

t2 x2 W = K   grad ax dx dt t1 x1

The differential form is the following:

a W  K   S  t x

Making the proper replacements in the The specific transport mechanisms relation above, we obtain the classical laws which describe particular, simple The more specific transport mechanisms transportation phenomena. are following: ion pump, transporting mole- With non stationary transportation we cules, ionic channels [2] and active transport understand those transportations where the through vesicles. value of the flow is modified in time from Exceptionally, the macromolecules are one point to the other. Making the right transported directly through the membrane. replacements in the relationship above we In the human body, this type of transfer is obtain the classical laws which describe the observed in the case of the membrane of the simple non stationary transportation endoplasmic reticulum for the proteins phenomena. synthesized at the level of this structure; in

Copyright 2020 KEI Journals. All Rights Reserved http://journals.ke-i.org/index.php/mra Janos Vincze et al. Medical Research Archives vol 8 issue 4. April 2020 Page 3 of 9 most cases, they are transported through the metabolism. This process was described with vesicles. electron microscope for iron penetration into I n 1 8 8 3 , Mecinikov described the erythroblasts. process through which leukocytes embed All these modes of transport, described as particles, microbial germs for example. This different cellular processes by the authors process was called by Mecinikov who observed them, have a unique phagocytosis. lysosomal mechanism emphasized by A s c h o f f and L a n d a u demonstrated D u v e (1966). The lysosomal apparatus in 1924 that if electronegative dyes are functions in connection with the membranes injected intravenously to animals, the size of of the endoplasmic reticulum and the cell which is several tens or hundreds of Å, these membrane from which it forms the walls of will be captured by cells of the macrophage the vesicles in which the intra- or extra- group, which they grouped in a system cellular particles are incorporated. [4] called reticuloendothelial (SRE). Thus, SRE Lysosomes are formations that are found is made up of cells that retain inside inside the cell in the form of corpuscles, electronegative colloidal substances injected originating in the endoplasmic reticulum into the circulation. (Novikoff), the system of channels that meet Other processes that take place in the with cisterns and vesicles, described by membrane have also been described: the Porter and Palade. They are of two types: process of rofeocytosis and the process of rough, constituting the ergastoplasm and cytopempsis. smooth. The process of cytopempsis, or the process Proteins synthesized in ergastoplasma are of transport via the vesicles, is also a transported along the channels of the vesicular process, initiated in the membrane endoplasmic reticulum and stored in dense area. The vesicle in this case constitutes a bodies, which therefore contain proteins means of transport of the substances through synthesized in the cell, having enzymatic cell, the contents of the vesicle as a whole functions of hydrolases (proteases, acid being transported through the cytoplasm, and phosphatases, etc.). The enzymes stored here then released. This process represents a are then transported in the form of vesicles differentiation of transport for the to Golgi’s reticular apparatus, in which the endothelial cells of blood capillaries. The lysosomes would form. cells that make up the capillary endothelium In the phagocytosis process, the lysosomes have the property, as researches have shown bind with the endocytic vesicle, which at the since 1953 (P a l a de), to capture from the membrane level has captured content from lumen of the capillary and to transport from the external living environment of the cell. the luminal internal part of the endothelial From this fusion a phagocytic vesicle is cells, through vesicles, blood content to the created, in which the foreign embedded basal membrane, in the interstitial fluid. [3] corpuscles are eventually digested with the The process of rofeocytosis is a process in participation of lysosomes. [5] which nutrient substances penetrate deeply into the cell surface, having a role in cellular

Endocytosis and exocytosis degenerated, old and malignant cells are embedded, and then destroyed. Cells capable Endocytosis consists of the transport of of phagocytosis are called phagocytes. In substances from the extracellular humans, they are of two types: macrophages environment to the interior of the cell with and neutrophils. Both result from precursor the help of a vesicle formed by the cell cells in the bone marrow, then circulate in membrane. Depending on the nature of the the blood for several days (where transported substance, endocytosis occurs as: macrophages are represented by monocytes, – phagocytosis - process present in the and polymorphomeleal leukocytes with whole animal scale, in humans, with special neutrophilic granulations make up about importance in the non-specific defense 60% of the white blood cells), after which processes, but also in the removal of old they move from the vessels into the tissues cells. It consists of the introduction of where they exercise the phagocytic function. particles through vesicles from the [7] Macrophages are also called histiocytes. extracellular environment into the cell; Phagocytes form in the body an eventual – pinocytosis - consists in the introduction of phagocytic system. This system has mobile liquid content through the vesicles into the components (circulating cells and especially cell (pinein = to drink) from the extracellular neutrophils) and sessile components, environment. Pinocytosis can be performed represented by macrophages. These are independently by receptors and mediated by found in the spleen, lymph nodes, liver receptors. (Kupffer cells), blood vessels, pulmonary Exocytosis is the process by which the alveoli, pleura, peritoneum. fusion of some vesicles of the cytoplasm However, the role of phagocytosis and the with the cell membrane is produced being reticulohistiocitary or reticulo-endothelial followed by the expulsion of the vesicle system in the defense processes of the body content outside the cell. Exocytosis is extremely important. The embedding of processes are described in the case of microbes by phagocytosis and their sub- secretory cells and at the terminal button sequent destruction by lysosomes is the last level in the case of synaptic transmission. stage of the fight of the organism against Transcytosis is the process of transporting infections. Antibiotics do not kill microbes, substances through the vesicles that, formed but only prevent their multiplication. at the apical or basal pole of the cell, pass Microbes are killed after phagocytosis. through the cytoplasm as such and release Usually the microbes colonize the interstitial the contents at the opposite pole of the cell. space of a tissue. Neutrophils and other This process is more active at the level of phagocytes are attracted to these sites by endothelial cells of the structure of the blood chemotactic signals emitted or induced by capillaries. [6] microbes. Phagocytes attach to the wall of In humans, phagocytosis plays an small vessels that irrigate the affected tissue. important role in the defense processes of They then pass through the vessel wall (the the body as this way the bacteria, parasites, post-capillary venule) and move to the site foreign substances, cellular debris, of infection, where they are embedded, and

Copyright 2020 KEI Journals. All Rights Reserved http://journals.ke-i.org/index.php/mra Janos Vincze et al. Medical Research Archives vol 8 issue 4. April 2020 Page 5 of 9 thus destroy the bacteria. the pinocytosis is the transportations of the big drops of liquid. Considering that in The phases of phagocitosis biology it is difficult to set apart the two aggregation states, lately the notion of Several phases of phagocytosis can be endocytosis has been used preferentially. distinguished: The pinocytosis phenomenon is found in a) Chemotactism is the directed movement of many types of cells, such as the phagocytes to the site of infection, as signals macrophages, the cells of the capillary serving bacterial components (proteins or endothelium, the cells of the sheath of lipids) or those of the body: e.g. serum Schwann etc. proteins that amplify the immune response. It is supposed that pinocytosis is the most b) The recognition and attachment of diffused active mechanism of phagocyte particles is achieved through the macromolecule transport, a hypothesis receptors of the phagocyte plasmalemma confirmed by the research made with the that recognize ligands from the particle electronic microscope. surface. In the case of phagocytosis of The pattern of the pinocytosis considers its senescent or malignant cells, carbohydrate static character, that is the probability to groups in the plasmalemma are recognized. form vesicles. [8] The pinocytosis and In the case of bacteria, it is often necessary phagocytosis phenomena – from to cover them with antibodies and/or mathematical point of wiev – are a complement, so they can be phagocytosed. probalistic manifestation. Likelihood of an c) Embedding is made by the phagocyte event, measured by the ratio of the emitting extensions called pseudopods, favourable cases – appearance of vesicles. which surround the particle and then close it The model of pinocytosis takes into completely in a vesicle internalized in the consideration its statistical character, i.e. the cytoplasm called phagosome. The probability of the formation of vesicle. The embedding process was compared to closing statistical model described for pinocytosis is a zipper. equally applicable to phagocytosis as well, d) The killing of phagocyte cells and their without any constrains. digestion is done after the fusion of the Let us take M as the number of vesicles on phagosome with a primary lysosome and the the dS surface of the cellular membrane, ce formation of the phagolysosome. and ci the concentration of the substance to be transported in the extra and intracellular A probabilistic model environment, in which case the variation of the possibility to form the nth vesicle Endocytosis is a special type of biological according to the type is given by the transport, which refers to the particles of equation: colloidal dimensions being engulfed by the dP t cells. We know two forms of endocytosis: K  n  ck . (Pn-1(t) – Pn(t)) + cb . (Pn+1(t) – phagocytosis and pinocytosis. Phagocytosis dt P (t)) ; means the transport of solid particles while n

1 ≤ n ≤ M why their sum appears in the formula. Since The nth vesicle can appear in two types: the probability of formation and detachment either there are n-1 vesicles and after the of the vesicles depends on the concentrations binding of a molecule to be transported on of the substances on both sides of the the surface of the membrane the nth vesicle membrane, the concentrations are is formed, or the membrane contains n+1 proportionality factors. K is a one-dimen- vesicles, of which one detaches towards the sional constant. Thus, we obtained a system cytoplasm and so n vesicles remain. of differential first degree equations, from From the probabilistic point of view, the which - knowing the limit conditions - we two methods are independent events, that is, obtain the following expression for n = 1:

dP t K  1  ck . (P0(t) – P1(t)) + cb . (P2(t) – P1(t)) ; dt

We cannot talk about pinocytosis unless there is at least one vesicle, that is why ce.P0 (t) = 0, and ci.P1(t) does not make sense. For this reason, when n = 1 these two terms disappear. For the limit condition n = M we will have:

dP t K  M  ck . (PM-1(t) – PM(t)) + cb . (PM+1(t) – PM(t)) ; dt

Expression in which two terms are null, can draw the same conclusion, since the life considering the maximum number of span of these vesicles is only a few seconds. vesicles. Although it is extremely difficult to [9] follow the dynamics of pinocytosis experi- mentally, this pattern gives us the dynamic The energetic level description of the process as well as the deduction of a few conclusions. The The mathematic pattern of the pinocytosis apparition of the pinocytic vesicles presents can be used without restrictions in the case of a statistic distribution. In the same way, the phagocytosis as well. Since endocytosis is a equation above allows the characterization specific active mechanism, we can suppose of the macromolecules in the cells in the that it also needs energy, probably supplied interstitial liquid, that is exocytosis, a by ATP as well. [10] The energy of the process which is found in all the secretive macroscopic bond is probably consumed for and excretory cells. the regeneration of the membrane structure, These deductions have been confirmed by respectively the formation of new membrane Palade’s research under the electronic units. microscope (1969), according to which the In killing bacteria, however, the oxidase in vesicles cannot be interpreted as sections the plasmalemma takes up an important role, passing through the pores of the membranes. which reaches, through the phagocytosis, the From the mathematical point of view one phagosome membrane. Oxidase catalyzes

Copyright 2020 KEI Journals. All Rights Reserved http://journals.ke-i.org/index.php/mra Janos Vincze et al. Medical Research Archives vol 8 issue 4. April 2020 Page 7 of 9 the following reaction: has not been digested in lysosomes. – – + Receptor-dependent pinocytosis or 2O2 + NADPH -> 2O2 + NADP + H – receptor-mediated endocytosis is performed The superoxide anion (O2 ) is generated with the help of plasmalemma receptors that inside the phagolysome, and is recognize specific macromolecules in the spontaneously converted into H2O2 extracellular fluid. The binding of the oxygenated water. Then, from the reaction – receptor ligand induces the diffusion of the O2 with H2O2 results the free hydroxyl - 1 receptor-ligand complex in special areas of radical (OH ) and singlet oxygen ( O2) that the plasmalemma, which appear as coated are highly reactive and toxic species that kill pits dressed, covered, on the cytoplasmic the microbes. [11] Due to the reaction face of special proteins. Coated pits, also catalyzed by the oxidase, there is a sharp called caveolea, then become vesicles of increase in the oxygen consumption of the endocytosis, which maintain for some time phaygocyte at the time of their activation after internalizing their clothing or covering, under the action of chemotactic factors from and are thus covered with a network of the outbreak of infection. proteins. The most well characterized protein is the clathrin, with a molecular weight of 180,000 daltons and with sequences The receptor theory conserved during evolution. Three clathrin molecules together with three smaller There are two types of pinocytosis: polypeptides join together in a characteristic receptor-independent and receptor- structure. From this basic unit, the clathrin dependent (or mediated). network is formed, like a net that dresses the Receptor-independent pinocytosis is also coated pits or the vesicles. Sometimes the called fluid phase endocytosis and is found clathrin network dresses only the coated pit, in many cells. For example, the macrophage so that when the vesicle is formed it will slip ingests within 30 minutes the equivalent of through the mesh of the network, becoming the entire plasmalemma, while fibroblasts a uncoated endocytosis vesicle, called recep- ingest one third of the plasmalemma, and tosome; to differentiate it from pynosome large quantities of macromolecules are (the vesicle of the receptor-independent introduced into the cell. As in this interval endocytosis). [12] the volume of the cell is kept constant, it Receptor-mediated endocytosis achieves a means that, simultaneously with the concentration of certain ligands in endocytosis, an equivalent amount of endocytosis vesicles, which is an important plasmalemma materials is added. Thus, part difference compared to receptor-independent of the endocytosis vesicles return to the pinocytosis, in which the concentration of plasmalemma, and the components of the the substances in the vesicles is equal to that plasmalemma are thus recirculated. The of the extracellular fluid. An important recycling of membranes consists in the process that occurs through receptor- fusion with plasmalemma of some mediated endocytosis is the capturing of endocytosis vesicles, the membrane of which cholesterol into animal cells.

carries out exchanges between plasma and Conclusion the interstitial fluid. In the transport of macromolecules, not only the size, but also A particular form of vesicle transport is the electrical charge and the chemical represented by the transcytosis, which carries properties of the molecule are important. out the transport of macromolecules through Thus, the vascular endothelium has an the capillary endothelial cells. Palade (1953) uneven distribution of electrical charges, was the first to describe by electron mic- with negatively charged microdomains. As roscopy in cytoplasm the endothelial cells proteins are also negatively charged, the vesicles that cross cells from one side to the preferred route of entry will be through the other; he suggested that these vesicles play an transcytosis vesicles. The chemical pro- important role in transporting plasma perties of the macromolecules to be macromoles outside the vascular bed. transported are also important, the vascular Transcytosis transport may occur either endothelium (and probably other plasma- through independent vesicles moving lemmas) can discriminate proteins based on through the endothelial cell from the luminal the chemical characteristics of the molecule. face (exposed to the interior of the vessel) to Proteins adsorbed on the surface of the the interstitial face (exposed to the interstitial plasmalemma are likely to be involved in fluid), or more rarely the vesicles merge into this discrimination. a channel that crosses the cell. Transcytosis

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