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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-polarized insertion mode. This insertion mechanism is denoted here through Srθ(0, p, q, m, α). It is polarized and non-radially symmetric and linked to the conditions,,and, with p and q as positive constant. Even for λ = v1/2D0, which produce capping-like effects, certain characterization of this mode can give substantial reductions in τdu.
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Figure 10: The pq-polarized insertion mode. This insertion mechanism is denoted here through Srθ(0, p, q, m, α). It is polarized and non-radially symmetric and linked to the conditions,,and, with p and q as positive constant. Even for λ = v1/2D0, which produce capping-like effects, certain characterization of this mode can give substantial reductions in τdu.

Mentions: We can deal with three different non-radially symmetric polarized insertion forms. One is obtained if we let and, then all recycling receptors will be sorted over the region Ωp(m, α) and we will be dealing with a p-polarized receptor insertion device denoted by means of Srθ(0, p, 0, m, α) (Figure 9 and Eq. A36). Furthermore, for a p-polarized mode, by reducing the area of the insertion region Ωp(m, α), we could accommodate all recycled receptors in a favorable position relative to the cross section of the coated pit perpendicular to flow streamlines. Then, we may conjecture that this will allow the effect of convection to be maximal for receptor trapping rate enhancement. But we found that this device could at best yield a narrow variation range of τλmα relative to τdu and not a relevant reduction in this value. In fact, for a p-polarized insertion mode with 0 < α ≤ π/6 and 1.1 ≤ m ≤ b/a, we found 1.01τdu ≤ τλmα ≤ 1.16τdu. Now, if we assume that 0 < α < π, and also that hold, then receptors will be sorted over the regions Ωp(m, α) and Ωq(m, α), resulting in another form of a non-radially symmetric polarized insertion mode. This is regarded here as a pq-polarized receptor insertion form and denoted through Srθ(0, p, q, m, α) (Figure 10 and Eq. A38). In particular, for m = 2.2, α = π/2, δp(m, α) = 0.20 and δq(m, π/2) = 0.80, we calculated τλmα = 0.45τdu. That is, a pq-polarized receptor insertion form could lead to a significant reduction of τdu. But if we now set and, then all recycling receptors will be delivered over the region Ωq(m, α), and we will have a third form of non-radially symmetric polarized insertion mode. This is named q-polarized insertion and is symbolized by means of Srθ(0, 0, q, m, α) (Figure 11 and Eq. A40). Additionally, this arrangement along with a slow convective transport (v = v0) and a normal diffusion process (D = D0)  could potentially induce a major reduction in τdu. In fact, if we set m = 2.0 and α = π/6 we obtain τλmα = 0.26τdu, which coincides with the plaque form insertion mode mentioned above. Hence, for the case λ = v0/D0 either polarized insertion over the regions Ωp(m, α) and Ωq(m, α) or over the region Ωq(m, α), both seem to provide an efficient mechanism for the reduction of 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-polarized insertion mode. This insertion mechanism is denoted here through Srθ(0, p, q, m, α). It is polarized and non-radially symmetric and linked to the conditions,,and, with p and q as positive constant. Even for λ = v1/2D0, which produce capping-like effects, certain characterization of this mode can give substantial reductions in τdu.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 10: The pq-polarized insertion mode. This insertion mechanism is denoted here through Srθ(0, p, q, m, α). It is polarized and non-radially symmetric and linked to the conditions,,and, with p and q as positive constant. Even for λ = v1/2D0, which produce capping-like effects, certain characterization of this mode can give substantial reductions in τdu.
Mentions: We can deal with three different non-radially symmetric polarized insertion forms. One is obtained if we let and, then all recycling receptors will be sorted over the region Ωp(m, α) and we will be dealing with a p-polarized receptor insertion device denoted by means of Srθ(0, p, 0, m, α) (Figure 9 and Eq. A36). Furthermore, for a p-polarized mode, by reducing the area of the insertion region Ωp(m, α), we could accommodate all recycled receptors in a favorable position relative to the cross section of the coated pit perpendicular to flow streamlines. Then, we may conjecture that this will allow the effect of convection to be maximal for receptor trapping rate enhancement. But we found that this device could at best yield a narrow variation range of τλmα relative to τdu and not a relevant reduction in this value. In fact, for a p-polarized insertion mode with 0 < α ≤ π/6 and 1.1 ≤ m ≤ b/a, we found 1.01τdu ≤ τλmα ≤ 1.16τdu. Now, if we assume that 0 < α < π, and also that hold, then receptors will be sorted over the regions Ωp(m, α) and Ωq(m, α), resulting in another form of a non-radially symmetric polarized insertion mode. This is regarded here as a pq-polarized receptor insertion form and denoted through Srθ(0, p, q, m, α) (Figure 10 and Eq. A38). In particular, for m = 2.2, α = π/2, δp(m, α) = 0.20 and δq(m, π/2) = 0.80, we calculated τλmα = 0.45τdu. That is, a pq-polarized receptor insertion form could lead to a significant reduction of τdu. But if we now set and, then all recycling receptors will be delivered over the region Ωq(m, α), and we will have a third form of non-radially symmetric polarized insertion mode. This is named q-polarized insertion and is symbolized by means of Srθ(0, 0, q, m, α) (Figure 11 and Eq. A40). Additionally, this arrangement along with a slow convective transport (v = v0) and a normal diffusion process (D = D0)  could potentially induce a major reduction in τdu. In fact, if we set m = 2.0 and α = π/6 we obtain τλmα = 0.26τdu, which coincides with the plaque form insertion mode mentioned above. Hence, for the case λ = v0/D0 either polarized insertion over the regions Ωp(m, α) and Ωq(m, α) or over the region Ωq(m, α), both seem to provide an efficient mechanism for the reduction of 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