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Surface aggregation patterns of LDL receptors near coated pits III: potential effects of combined retrograde membrane flow-diffusion and a polarized-insertion mechanism.

Echavarria-Heras H, Leal-Ramirez C, Castillo O - Theor Biol Med Model (2014)

Bottom Line: We also project the resulting display of unbound receptors on the cell membrane.Our results show that, in spite of its efficiency as a possible device for enhancement of the rate of receptor trapping, polarized insertion nevertheless fails to induce the formation of steady-state clusters of receptor on the cell membrane.Moreover, for appropriate values of the flow strength-diffusion ratio, the predicted steady-state distribution of receptors on the surface was found to be consistent with the phenomenon of capping.

View Article: PubMed Central - HTML - PubMed

Affiliation: Modeling and Theoretical Analysis Research Group, Centro de Investigación Científica y de Educación Superior de Ensenada, Carretera Ensenada-Tijuana No, 3818, Zona Playitas, C, P, 22869 Ensenada, Baja California, México. heheras@icloud.com.

ABSTRACT
Although the process of endocytosis of the low density lipoprotein (LDL) macromolecule and its receptor have been the subject of intense experimental research and modeling, there are still conflicting hypotheses and even conflicting data regarding the way receptors are transported to coated pits, the manner by which receptors are inserted before they aggregate in coated pits, and the display of receptors on the cell surface. At first it was considered that LDL receptors in human fibroblasts are inserted at random locations and then transported by diffusion toward coated pits. But experiments have not ruled out the possibility that the true rate of accumulation of LDL receptors in coated pits might be faster than predicted on the basis of pure diffusion and uniform reinsertion over the entire cell surface. It has been claimed that recycled LDL receptors are inserted preferentially in regions where coated pits form, with display occurring predominantly as groups of loosely associated units. Another mechanism that has been proposed by experimental cell biologists which might affect the accumulation of receptors in coated pits is a retrograde membrane flow. This is essentially linked to a polarized receptor insertion mode and also to the capping phenomenon, characterized by the formation of large patches of proteins that passively flow away from the regions of membrane exocytosis. In this contribution we calculate the mean travel time of LDL receptors to coated pits as determined by the ratio of flow strength to diffusion-coefficient, as well as by polarized-receptor insertion. We also project the resulting display of unbound receptors on the cell membrane. We found forms of polarized insertion that could potentially reduce the mean capture time of LDL receptors by coated pits which is controlled by diffusion and uniform insertion. Our results show that, in spite of its efficiency as a possible device for enhancement of the rate of receptor trapping, polarized insertion nevertheless fails to induce the formation of steady-state clusters of receptor on the cell membrane. Moreover, for appropriate values of the flow strength-diffusion ratio, the predicted steady-state distribution of receptors on the surface was found to be consistent with the phenomenon of capping.

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The pq-uniform insertion mode. This is denoted by means of the symbol Srθ(0, c, c, m, π), and obtained by setting the conditions and, with c a positive constant.
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Figure 3: The pq-uniform insertion mode. This is denoted by means of the symbol Srθ(0, c, c, m, π), and obtained by setting the conditions and, with c a positive constant.

Mentions: In the present setting, a uniform insertion-rate function can be acquired by, for instance taking α = 0, m = b/a and, where c is a positive constant and. This representation is known here as a c-uniform insertion mode (Figure 2 and Eq. A22). A second description of a uniform insertion mode is what we call a pq-uniform rate function, in which receptors are inserted solely over the regions Ωp(m, π) and Ωq(m, π); this is realized by setting, where c is a positive constant (Figure 3 and Eq. A24). Finally, a description that we refer to as cpq-uniform insertion is achieved by sorting receptors over the three disjoint regions Ωc(m, α), Ωp(m, α), Ωq(m, α)  with, where c is a positive constant (Figure 4 and Eq. A26). Consistently, for the case where no convective flow is present (v = 0) and receptors diffuse normally (D = D0), all these representations indistinctively yield τλmα = τdu.


Surface aggregation patterns of LDL receptors near coated pits III: potential effects of combined retrograde membrane flow-diffusion and a polarized-insertion mechanism.

Echavarria-Heras H, Leal-Ramirez C, Castillo O - Theor Biol Med Model (2014)

The pq-uniform insertion mode. This is denoted by means of the symbol Srθ(0, c, c, m, π), and obtained by setting the conditions and, with c a positive constant.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4048462&req=5

Figure 3: The pq-uniform insertion mode. This is denoted by means of the symbol Srθ(0, c, c, m, π), and obtained by setting the conditions and, with c a positive constant.
Mentions: In the present setting, a uniform insertion-rate function can be acquired by, for instance taking α = 0, m = b/a and, where c is a positive constant and. This representation is known here as a c-uniform insertion mode (Figure 2 and Eq. A22). A second description of a uniform insertion mode is what we call a pq-uniform rate function, in which receptors are inserted solely over the regions Ωp(m, π) and Ωq(m, π); this is realized by setting, where c is a positive constant (Figure 3 and Eq. A24). Finally, a description that we refer to as cpq-uniform insertion is achieved by sorting receptors over the three disjoint regions Ωc(m, α), Ωp(m, α), Ωq(m, α)  with, where c is a positive constant (Figure 4 and Eq. A26). Consistently, for the case where no convective flow is present (v = 0) and receptors diffuse normally (D = D0), all these representations indistinctively yield τλmα = τdu.

Bottom Line: We also project the resulting display of unbound receptors on the cell membrane.Our results show that, in spite of its efficiency as a possible device for enhancement of the rate of receptor trapping, polarized insertion nevertheless fails to induce the formation of steady-state clusters of receptor on the cell membrane.Moreover, for appropriate values of the flow strength-diffusion ratio, the predicted steady-state distribution of receptors on the surface was found to be consistent with the phenomenon of capping.

View Article: PubMed Central - HTML - PubMed

Affiliation: Modeling and Theoretical Analysis Research Group, Centro de Investigación Científica y de Educación Superior de Ensenada, Carretera Ensenada-Tijuana No, 3818, Zona Playitas, C, P, 22869 Ensenada, Baja California, México. heheras@icloud.com.

ABSTRACT
Although the process of endocytosis of the low density lipoprotein (LDL) macromolecule and its receptor have been the subject of intense experimental research and modeling, there are still conflicting hypotheses and even conflicting data regarding the way receptors are transported to coated pits, the manner by which receptors are inserted before they aggregate in coated pits, and the display of receptors on the cell surface. At first it was considered that LDL receptors in human fibroblasts are inserted at random locations and then transported by diffusion toward coated pits. But experiments have not ruled out the possibility that the true rate of accumulation of LDL receptors in coated pits might be faster than predicted on the basis of pure diffusion and uniform reinsertion over the entire cell surface. It has been claimed that recycled LDL receptors are inserted preferentially in regions where coated pits form, with display occurring predominantly as groups of loosely associated units. Another mechanism that has been proposed by experimental cell biologists which might affect the accumulation of receptors in coated pits is a retrograde membrane flow. This is essentially linked to a polarized receptor insertion mode and also to the capping phenomenon, characterized by the formation of large patches of proteins that passively flow away from the regions of membrane exocytosis. In this contribution we calculate the mean travel time of LDL receptors to coated pits as determined by the ratio of flow strength to diffusion-coefficient, as well as by polarized-receptor insertion. We also project the resulting display of unbound receptors on the cell membrane. We found forms of polarized insertion that could potentially reduce the mean capture time of LDL receptors by coated pits which is controlled by diffusion and uniform insertion. Our results show that, in spite of its efficiency as a possible device for enhancement of the rate of receptor trapping, polarized insertion nevertheless fails to induce the formation of steady-state clusters of receptor on the cell membrane. Moreover, for appropriate values of the flow strength-diffusion ratio, the predicted steady-state distribution of receptors on the surface was found to be consistent with the phenomenon of capping.

Show MeSH
Related in: MedlinePlus