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Glial scar size, inhibitor concentration, and growth of regenerating axons after spinal cord transection.

Zhu W, Sun Y, Chen X, Feng S - Neural Regen Res (2012)

Bottom Line: A three-dimensional lattice Boltzmann method was used for numerical simulation.Results demonstrated that (1) a larger glial scar and a higher release rate of inhibitor resulted in a reduced axonal growth rate. (2) The axonal growth rate depended on the ratio of inhibitor to promoter concentrations at the growth cones.When the average ratio was < 1.5, regenerating axons were able to grow and successfully contact target cells.

View Article: PubMed Central - PubMed

Affiliation: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China.

ABSTRACT
A mathematical model has been formulated in accordance with cell chemotaxis and relevant experimental data. A three-dimensional lattice Boltzmann method was used for numerical simulation. The present study observed the effects of glial scar size and inhibitor concentration on regenerative axonal growth following spinal cord transection. The simulation test comprised two parts: (1) when release rates of growth inhibitor and promoter were constant, the effects of glial scar size on axonal growth rate were analyzed, and concentrations of inhibitor and promoters located at the moving growth cones were recorded. (2) When the glial scar size was constant, the effects of inhibitor and promoter release rates on axonal growth rate were analyzed, and inhibitor and promoter concentrations at the moving growth cones were recorded. Results demonstrated that (1) a larger glial scar and a higher release rate of inhibitor resulted in a reduced axonal growth rate. (2) The axonal growth rate depended on the ratio of inhibitor to promoter concentrations at the growth cones. When the average ratio was < 1.5, regenerating axons were able to grow and successfully contact target cells.

No MeSH data available.


Related in: MedlinePlus

Changes in inhibitor concentration (ρ2, Y-axis) and helper factor concentration (ρ3, Y-axis) in the No.1 growth cone of regenerating axons with time of axonal growth (X-axis). A and B refer to growth cone of No.1 axon in Figures 2A and B, respectively.A (Figure 2A) refers to normal axonal growth (blank control). The inhibitor concentration ρ2 and helper factor concentration ρ3 are almost mirror symmetry with time to successful connection of growth cone and target cells. A balance point appears immediately prior to connection and upon successful connection.B (Figure 2B) represents a large glial scar and high release rate of inhibitors. ρ2 represents a process of increase, fluctuation, increase, decrease, and a stable increase over time to when the growth cone ceases to grow, suggesting that axons exhibit motility and avoid high inhibiting concentrations.However, the axons stop growing due to high inhibitor concentrations in the microenvironment, and helper factor concentration ρ3 was low.
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Figure 4: Changes in inhibitor concentration (ρ2, Y-axis) and helper factor concentration (ρ3, Y-axis) in the No.1 growth cone of regenerating axons with time of axonal growth (X-axis). A and B refer to growth cone of No.1 axon in Figures 2A and B, respectively.A (Figure 2A) refers to normal axonal growth (blank control). The inhibitor concentration ρ2 and helper factor concentration ρ3 are almost mirror symmetry with time to successful connection of growth cone and target cells. A balance point appears immediately prior to connection and upon successful connection.B (Figure 2B) represents a large glial scar and high release rate of inhibitors. ρ2 represents a process of increase, fluctuation, increase, decrease, and a stable increase over time to when the growth cone ceases to grow, suggesting that axons exhibit motility and avoid high inhibiting concentrations.However, the axons stop growing due to high inhibitor concentrations in the microenvironment, and helper factor concentration ρ3 was low.

Mentions: Figures 3A, 4A, and 5A list concentrations of type 1–3 factors at the position where axon No. 1 existed in Figure 2A. In addition, the figures show changes in movement speed of the growth cone and time of axonal growth. A in all figures refers to normal axonal growth (blank control), glial scars did not chemically or physically differ from the common substrate). Promoter concentrations (Figure 3A) increased exponentially with time as the growth cone reached the target cells (release source), and concentrations greatly fluctuated near the target cells. Axons reached the target cells, which generated promoters and transported them into the neuronal cell body via the axon. Therefore, promoter concentrations were low around the target cells and, therefore, not attractive for other axons. In addition, other axons grew towards the region with high concentrations of the promoter. Inhibitor concentration (ρ2) slightly differed from the helper factor concentration (ρ3) generated by the substrate (including glial scar), which was determined by the release rate pattern of type 2 and 3 factors (equations 1–3 in the methods section). A balance point appeared at approximately 3 000 minutes (Figure 4A), and an additional balance point appeared when the axons successfully contacted the target cells. Axonal growth velocity (Figure 5A) was determintly determined according to promoter concentration gradient (ρ1), which was generated by the target cells, and velocity changes were consistent with ρ1 changes. At the beginning, target signals were weak, but then slowly advanced and sped up. Influenced by the connection of other axons to target cells, the touch time was increased and forward velocity became slow. Subsequently, velocity increased when the axons nearly reached the target cells, although velocity remained within 0.01–0.5 μm/s. All axons in Figure 2A successfully contacted target cells; this took 4068 minutes.


Glial scar size, inhibitor concentration, and growth of regenerating axons after spinal cord transection.

Zhu W, Sun Y, Chen X, Feng S - Neural Regen Res (2012)

Changes in inhibitor concentration (ρ2, Y-axis) and helper factor concentration (ρ3, Y-axis) in the No.1 growth cone of regenerating axons with time of axonal growth (X-axis). A and B refer to growth cone of No.1 axon in Figures 2A and B, respectively.A (Figure 2A) refers to normal axonal growth (blank control). The inhibitor concentration ρ2 and helper factor concentration ρ3 are almost mirror symmetry with time to successful connection of growth cone and target cells. A balance point appears immediately prior to connection and upon successful connection.B (Figure 2B) represents a large glial scar and high release rate of inhibitors. ρ2 represents a process of increase, fluctuation, increase, decrease, and a stable increase over time to when the growth cone ceases to grow, suggesting that axons exhibit motility and avoid high inhibiting concentrations.However, the axons stop growing due to high inhibitor concentrations in the microenvironment, and helper factor concentration ρ3 was low.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4308747&req=5

Figure 4: Changes in inhibitor concentration (ρ2, Y-axis) and helper factor concentration (ρ3, Y-axis) in the No.1 growth cone of regenerating axons with time of axonal growth (X-axis). A and B refer to growth cone of No.1 axon in Figures 2A and B, respectively.A (Figure 2A) refers to normal axonal growth (blank control). The inhibitor concentration ρ2 and helper factor concentration ρ3 are almost mirror symmetry with time to successful connection of growth cone and target cells. A balance point appears immediately prior to connection and upon successful connection.B (Figure 2B) represents a large glial scar and high release rate of inhibitors. ρ2 represents a process of increase, fluctuation, increase, decrease, and a stable increase over time to when the growth cone ceases to grow, suggesting that axons exhibit motility and avoid high inhibiting concentrations.However, the axons stop growing due to high inhibitor concentrations in the microenvironment, and helper factor concentration ρ3 was low.
Mentions: Figures 3A, 4A, and 5A list concentrations of type 1–3 factors at the position where axon No. 1 existed in Figure 2A. In addition, the figures show changes in movement speed of the growth cone and time of axonal growth. A in all figures refers to normal axonal growth (blank control), glial scars did not chemically or physically differ from the common substrate). Promoter concentrations (Figure 3A) increased exponentially with time as the growth cone reached the target cells (release source), and concentrations greatly fluctuated near the target cells. Axons reached the target cells, which generated promoters and transported them into the neuronal cell body via the axon. Therefore, promoter concentrations were low around the target cells and, therefore, not attractive for other axons. In addition, other axons grew towards the region with high concentrations of the promoter. Inhibitor concentration (ρ2) slightly differed from the helper factor concentration (ρ3) generated by the substrate (including glial scar), which was determined by the release rate pattern of type 2 and 3 factors (equations 1–3 in the methods section). A balance point appeared at approximately 3 000 minutes (Figure 4A), and an additional balance point appeared when the axons successfully contacted the target cells. Axonal growth velocity (Figure 5A) was determintly determined according to promoter concentration gradient (ρ1), which was generated by the target cells, and velocity changes were consistent with ρ1 changes. At the beginning, target signals were weak, but then slowly advanced and sped up. Influenced by the connection of other axons to target cells, the touch time was increased and forward velocity became slow. Subsequently, velocity increased when the axons nearly reached the target cells, although velocity remained within 0.01–0.5 μm/s. All axons in Figure 2A successfully contacted target cells; this took 4068 minutes.

Bottom Line: A three-dimensional lattice Boltzmann method was used for numerical simulation.Results demonstrated that (1) a larger glial scar and a higher release rate of inhibitor resulted in a reduced axonal growth rate. (2) The axonal growth rate depended on the ratio of inhibitor to promoter concentrations at the growth cones.When the average ratio was < 1.5, regenerating axons were able to grow and successfully contact target cells.

View Article: PubMed Central - PubMed

Affiliation: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China.

ABSTRACT
A mathematical model has been formulated in accordance with cell chemotaxis and relevant experimental data. A three-dimensional lattice Boltzmann method was used for numerical simulation. The present study observed the effects of glial scar size and inhibitor concentration on regenerative axonal growth following spinal cord transection. The simulation test comprised two parts: (1) when release rates of growth inhibitor and promoter were constant, the effects of glial scar size on axonal growth rate were analyzed, and concentrations of inhibitor and promoters located at the moving growth cones were recorded. (2) When the glial scar size was constant, the effects of inhibitor and promoter release rates on axonal growth rate were analyzed, and inhibitor and promoter concentrations at the moving growth cones were recorded. Results demonstrated that (1) a larger glial scar and a higher release rate of inhibitor resulted in a reduced axonal growth rate. (2) The axonal growth rate depended on the ratio of inhibitor to promoter concentrations at the growth cones. When the average ratio was < 1.5, regenerating axons were able to grow and successfully contact target cells.

No MeSH data available.


Related in: MedlinePlus