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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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Surface aggregation patterns of unbound LDL receptors associated with different values of the fundamental ratio λ and non-radially symmetric-polarized insertion modes. a) the surface pattern made by λ = v1/2D0 and the q-polarized insertion mode Srθ(0, 0, q, m, α), with m = 2.3, δq(m, α) = 1 and α = π/4; b) surface pattern associated with the case λ = v1/2D1 and the p-polarized insertion mode Srθ(0, p, 0, m, α) with α = π/6, m = 9.5, and δp(m, α) = 1; c) the surface aggregation pattern formed by λ = v1/2Dext and q-polarized insertion Srθ(0, p, q, m, α) with m = 1.2, α = π/6 and δq(m, α) = 1; d) the surface receptor pattern for λ = v1/2Dext and p-polarized insertion Srθ(0, p, q, m, α) with m = 9.5, α = π/4 and δp(m, α) = 1. The patterns shown are consistent with the capping phenomena; that is, when convection is fast (v = v1) and diffusion is normal (D = D0) a graduated distribution in the direction of flow streamlines is observed, a) and b). But in the presence of a fast convective transport, suitable values of the diffusion coefficient (e. g. D = Dext) can reverse the capping effect and induce an effective randomization of the distribution of unbound LDL receptors, c) and d). In any event, in the presence of a retrograde membrane flow, no receptor surface clusters are formed.
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Figure 12: Surface aggregation patterns of unbound LDL receptors associated with different values of the fundamental ratio λ and non-radially symmetric-polarized insertion modes. a) the surface pattern made by λ = v1/2D0 and the q-polarized insertion mode Srθ(0, 0, q, m, α), with m = 2.3, δq(m, α) = 1 and α = π/4; b) surface pattern associated with the case λ = v1/2D1 and the p-polarized insertion mode Srθ(0, p, 0, m, α) with α = π/6, m = 9.5, and δp(m, α) = 1; c) the surface aggregation pattern formed by λ = v1/2Dext and q-polarized insertion Srθ(0, p, q, m, α) with m = 1.2, α = π/6 and δq(m, α) = 1; d) the surface receptor pattern for λ = v1/2Dext and p-polarized insertion Srθ(0, p, q, m, α) with m = 9.5, α = π/4 and δp(m, α) = 1. The patterns shown are consistent with the capping phenomena; that is, when convection is fast (v = v1) and diffusion is normal (D = D0) a graduated distribution in the direction of flow streamlines is observed, a) and b). But in the presence of a fast convective transport, suitable values of the diffusion coefficient (e. g. D = Dext) can reverse the capping effect and induce an effective randomization of the distribution of unbound LDL receptors, c) and d). In any event, in the presence of a retrograde membrane flow, no receptor surface clusters are formed.

Mentions: For the insertion-transport mechanism for LDL receptors under consideration, we also address here the theoretical exploration of their consequent display on the cell surface. A capping-like surface display should manifest as a graduated concentration of receptors in the direction of flow streamlines. Figure 12 displays the surface aggregation patterns of receptors that result when a polarized reinsertion mode is considered. The combination of polarized insertion, fast convective transport of rate v = v1 and a relatively slow diffusion process such as one associated to D0 can be observed to produce a marked gradient in the distribution of unbound receptors (Figure 12a and b). This is consistent with the conceptual model for the capping phenomenon presented by Bretscher[14]. Further, and in concurrence with that author, the present model explains this gradient as being induced by a relative dominance of convection over diffusion; that is, an arrangement which precludes an effective randomization of the surface-receptor distribution. Thus, in the presence of a retrograde membrane flow with typical strength v = v1, even single LDL particles having a diffusion coefficient value D = D0 —which is considered normal—would produce a capping-like cell surface distribution; thus precluding both a uniform distribution and the display of clusters of unbound receptors on the surface. Even in the presence of a fast convective transport, a suitably fast diffusion process can reverse the capping effects (Figures 12c and d).


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)

Surface aggregation patterns of unbound LDL receptors associated with different values of the fundamental ratio λ and non-radially symmetric-polarized insertion modes. a) the surface pattern made by λ = v1/2D0 and the q-polarized insertion mode Srθ(0, 0, q, m, α), with m = 2.3, δq(m, α) = 1 and α = π/4; b) surface pattern associated with the case λ = v1/2D1 and the p-polarized insertion mode Srθ(0, p, 0, m, α) with α = π/6, m = 9.5, and δp(m, α) = 1; c) the surface aggregation pattern formed by λ = v1/2Dext and q-polarized insertion Srθ(0, p, q, m, α) with m = 1.2, α = π/6 and δq(m, α) = 1; d) the surface receptor pattern for λ = v1/2Dext and p-polarized insertion Srθ(0, p, q, m, α) with m = 9.5, α = π/4 and δp(m, α) = 1. The patterns shown are consistent with the capping phenomena; that is, when convection is fast (v = v1) and diffusion is normal (D = D0) a graduated distribution in the direction of flow streamlines is observed, a) and b). But in the presence of a fast convective transport, suitable values of the diffusion coefficient (e. g. D = Dext) can reverse the capping effect and induce an effective randomization of the distribution of unbound LDL receptors, c) and d). In any event, in the presence of a retrograde membrane flow, no receptor surface clusters are formed.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 12: Surface aggregation patterns of unbound LDL receptors associated with different values of the fundamental ratio λ and non-radially symmetric-polarized insertion modes. a) the surface pattern made by λ = v1/2D0 and the q-polarized insertion mode Srθ(0, 0, q, m, α), with m = 2.3, δq(m, α) = 1 and α = π/4; b) surface pattern associated with the case λ = v1/2D1 and the p-polarized insertion mode Srθ(0, p, 0, m, α) with α = π/6, m = 9.5, and δp(m, α) = 1; c) the surface aggregation pattern formed by λ = v1/2Dext and q-polarized insertion Srθ(0, p, q, m, α) with m = 1.2, α = π/6 and δq(m, α) = 1; d) the surface receptor pattern for λ = v1/2Dext and p-polarized insertion Srθ(0, p, q, m, α) with m = 9.5, α = π/4 and δp(m, α) = 1. The patterns shown are consistent with the capping phenomena; that is, when convection is fast (v = v1) and diffusion is normal (D = D0) a graduated distribution in the direction of flow streamlines is observed, a) and b). But in the presence of a fast convective transport, suitable values of the diffusion coefficient (e. g. D = Dext) can reverse the capping effect and induce an effective randomization of the distribution of unbound LDL receptors, c) and d). In any event, in the presence of a retrograde membrane flow, no receptor surface clusters are formed.
Mentions: For the insertion-transport mechanism for LDL receptors under consideration, we also address here the theoretical exploration of their consequent display on the cell surface. A capping-like surface display should manifest as a graduated concentration of receptors in the direction of flow streamlines. Figure 12 displays the surface aggregation patterns of receptors that result when a polarized reinsertion mode is considered. The combination of polarized insertion, fast convective transport of rate v = v1 and a relatively slow diffusion process such as one associated to D0 can be observed to produce a marked gradient in the distribution of unbound receptors (Figure 12a and b). This is consistent with the conceptual model for the capping phenomenon presented by Bretscher[14]. Further, and in concurrence with that author, the present model explains this gradient as being induced by a relative dominance of convection over diffusion; that is, an arrangement which precludes an effective randomization of the surface-receptor distribution. Thus, in the presence of a retrograde membrane flow with typical strength v = v1, even single LDL particles having a diffusion coefficient value D = D0 —which is considered normal—would produce a capping-like cell surface distribution; thus precluding both a uniform distribution and the display of clusters of unbound receptors on the surface. Even in the presence of a fast convective transport, a suitably fast diffusion process can reverse the capping effects (Figures 12c and d).

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