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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 p-peripheral insertion mode. An insertion form denoted here by means of Srθ(0, p, 0, m, π). It is a radially symmetric and polarized and linked to the case,, and, with p a positive constant.
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Figure 8: The p-peripheral insertion mode. An insertion form denoted here by means of Srθ(0, p, 0, m, π). It is a radially symmetric and polarized and linked to the case,, and, with p a positive constant.

Mentions: For the case in which convective transport is moderate (v = v0) and receptors diffuse normally (D = D0), that is, the flow strength to diffusion ratio λ has a value λ = v0/2D0, calculating τλmα as given by equation (B27) for Srθ(c, p, q, m, α) where insertion is uniform over all of Ω, we obtained τλmα = 1.003 τdu. Hence, the present model predicts that if LDL receptors diffuse normally, a retrograde membrane flow having strength comparable to v0 would have an insignificant effect on τdu. But for that same convection-to-diffusion ratio, we found that a locally uniform insertion mode can prompt greater receptor trapping rates than those linked to uniform insertion all over Ω. But now suppose that receptor insertion takes place over the regions Ωc(m, α), Ωp(m, α) and Ωq(m, α), at different constant rates and; this results in what we term here a cpq-locally uniform insertion mode (Figure 5 and Eq. A28). Then, if for instance we choose m = 1.5, α = π/2, δc(m, α) = 0.10, δp(m, α) = 0.30 and δq(m, α) = 0.60, the model yields τλmα = 0.49τdu, which amounts to an important reduction of τdu. For α = π we obtain what we label here as a pq-locally uniform insertion form (Figure 6 and Eq. 30) denoted by the symbol Srθ(0, p, q, m, π). Receptors are inserted in a radially symmetric manner over each of the regions Ωq(m, π) and Ωp(m, π), but through different constant rates and For m = 2.0, δp(m, π) = 0.20 and δq(m, π) = 0.80, the model yields τλmα = 0.41τdu. Now, since for a pq-locally uniform insertion form we have δp(m, π) + δq(m, π) = 1, then letting δp(m, π) approach zero, receptor insertion will be gradually accommodated within the region Ωq(m, α)  so that eventually, when δp(m, π) vanishes, we will obtain what we identify as a q-plaque form insertion mode denoted by means of the symbol Srθ(0, 0, q, m, π) (Figure 7 and Eq. A32). This is actually the plaque-form insertion mechanism envisioned by Wofsy et al.[40] for modeling preferential insertion as conceived by Robeneck and Hesz[39]. For λ = v0/D0, and m = 2.0, the mode Srθ(0, 0, q, m, π) yields τλmα = 0.26τdu, again a noticeable reduction in τdu. This mode is radially symmetric and can be already considered as a form of polarized insertion. Similarly, if we initially chose a locally uniform mode Srθ(0, p, q, m, π), then letting δq(m, π) approach zero we will force receptors to be mainly sorted over the Ωp(m, π), region and in due course when δq(m, π) vanishes will produce what we call a p-peripheral insertion mode symbolized by means of Srθ(0, p, 0, m, π) (Figure 8 and Eq. A34). This insertion rate function is a peripheral form of polarized insertion; receptors are inserted in an annulus contiguous to the outer boundary of Ω. For λ = v0/D0, peripheral insertion yields τλmα ≥ 1.003 τdu with the lower bound of 1.003 τdu attained in the limiting case when m approaches one. Hence, if enhancement of LDL receptor trapping rate is required, a peripheral insertion mode for m > 1 turns out to be an inefficient mechanism. For instance taking λ = v0/2D0, and m = 9.7 we obtain τλmα = 1.15τdu.


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 p-peripheral insertion mode. An insertion form denoted here by means of Srθ(0, p, 0, m, π). It is a radially symmetric and polarized and linked to the case,, and, with p 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 8: The p-peripheral insertion mode. An insertion form denoted here by means of Srθ(0, p, 0, m, π). It is a radially symmetric and polarized and linked to the case,, and, with p a positive constant.
Mentions: For the case in which convective transport is moderate (v = v0) and receptors diffuse normally (D = D0), that is, the flow strength to diffusion ratio λ has a value λ = v0/2D0, calculating τλmα as given by equation (B27) for Srθ(c, p, q, m, α) where insertion is uniform over all of Ω, we obtained τλmα = 1.003 τdu. Hence, the present model predicts that if LDL receptors diffuse normally, a retrograde membrane flow having strength comparable to v0 would have an insignificant effect on τdu. But for that same convection-to-diffusion ratio, we found that a locally uniform insertion mode can prompt greater receptor trapping rates than those linked to uniform insertion all over Ω. But now suppose that receptor insertion takes place over the regions Ωc(m, α), Ωp(m, α) and Ωq(m, α), at different constant rates and; this results in what we term here a cpq-locally uniform insertion mode (Figure 5 and Eq. A28). Then, if for instance we choose m = 1.5, α = π/2, δc(m, α) = 0.10, δp(m, α) = 0.30 and δq(m, α) = 0.60, the model yields τλmα = 0.49τdu, which amounts to an important reduction of τdu. For α = π we obtain what we label here as a pq-locally uniform insertion form (Figure 6 and Eq. 30) denoted by the symbol Srθ(0, p, q, m, π). Receptors are inserted in a radially symmetric manner over each of the regions Ωq(m, π) and Ωp(m, π), but through different constant rates and For m = 2.0, δp(m, π) = 0.20 and δq(m, π) = 0.80, the model yields τλmα = 0.41τdu. Now, since for a pq-locally uniform insertion form we have δp(m, π) + δq(m, π) = 1, then letting δp(m, π) approach zero, receptor insertion will be gradually accommodated within the region Ωq(m, α)  so that eventually, when δp(m, π) vanishes, we will obtain what we identify as a q-plaque form insertion mode denoted by means of the symbol Srθ(0, 0, q, m, π) (Figure 7 and Eq. A32). This is actually the plaque-form insertion mechanism envisioned by Wofsy et al.[40] for modeling preferential insertion as conceived by Robeneck and Hesz[39]. For λ = v0/D0, and m = 2.0, the mode Srθ(0, 0, q, m, π) yields τλmα = 0.26τdu, again a noticeable reduction in τdu. This mode is radially symmetric and can be already considered as a form of polarized insertion. Similarly, if we initially chose a locally uniform mode Srθ(0, p, q, m, π), then letting δq(m, π) approach zero we will force receptors to be mainly sorted over the Ωp(m, π), region and in due course when δq(m, π) vanishes will produce what we call a p-peripheral insertion mode symbolized by means of Srθ(0, p, 0, m, π) (Figure 8 and Eq. A34). This insertion rate function is a peripheral form of polarized insertion; receptors are inserted in an annulus contiguous to the outer boundary of Ω. For λ = v0/D0, peripheral insertion yields τλmα ≥ 1.003 τdu with the lower bound of 1.003 τdu attained in the limiting case when m approaches one. Hence, if enhancement of LDL receptor trapping rate is required, a peripheral insertion mode for m > 1 turns out to be an inefficient mechanism. For instance taking λ = v0/2D0, and m = 9.7 we obtain τλmα = 1.15τdu.

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