1. Kinetics of Prion Growth
Thorsten Pöschel, Nikolai V. Brilliantov, Cornelius Frömmel 
Biophysical Journal 
Volume 85, Issue 6, Pages (December 2003)
DOI: /S (03)
Copyright © 2003 The Biophysical Society Terms and Conditions

2. Figure 1
Sketch of the prion aggregate growth model after Masel et al. (1999) but modified. For explanation see text.
Biophysical Journal  , DOI: ( /S (03) )
Copyright © 2003 The Biophysical Society Terms and Conditions

3. Figure 2
Distribution of polymers wi≡yi/y over the polymer length i for fixed number of monomers x0=500. We obtain excellent agreement between the analytical result Eq. 26 (line) and the results of a numerical simulation (circles). The parameters are n=6, a=0.05, b=9×10−4, and β=0.015.
Biophysical Journal  , DOI: ( /S (03) )
Copyright © 2003 The Biophysical Society Terms and Conditions

4. Figure 3
Evolution of the average size s=z(t)/y(t) of PrPsc polymers due to Eq. 30 (line) and results of a simulation (circles). The parameters are n=6, a=0.05, b=9×10−4, and β= The initial size is s(0)=10.
Biophysical Journal  , DOI: ( /S (03) )
Copyright © 2003 The Biophysical Society Terms and Conditions

5. Figure 4
The average growth velocity s˙ over the average size s due to Eq. 29. The parameters are n=6, a=0.015, b=0.0009, β=0.025, and x0=500.
Biophysical Journal  , DOI: ( /S (03) )
Copyright © 2003 The Biophysical Society Terms and Conditions

6. Figure 5
PrPsc polymer growth scenarios for the case s*<s1. The parameters are n=6, a=0.05, b=9×10−4, and β=0.015, which corresponds to s*=66.44 and s1= (Top) s(0)<s* (y10(0)=5×105); (middle) s(0)>s* (y25(0)=8×103); and (bottom) s(0)>s1 (y200(0)=25,000). In all cases the initial inoculation is z(0)=5×106.
Biophysical Journal  , DOI: ( /S (03) )
Copyright © 2003 The Biophysical Society Terms and Conditions

7. Figure 6
PrPsc polymer growth scenarios for the case s*>s1. The parameters are the same as in Fig. 5 except for a=0.1, which corresponds to s*= and s1= (Top) s(0)<s1 (y10(0)=5×105); (middle) s*>s(0)>s1 (y100(0)=5×104); and (bottom) s(0)>s* (y500(0)=104). In all cases the total initial inoculation is z(0)=5×106.
Biophysical Journal  , DOI: ( /S (03) )
Copyright © 2003 The Biophysical Society Terms and Conditions

8. Figure 7
Evolution of the number of monomers x=x(t). The simulation starts with x(0)=100 monomers and relaxes within a very short time (which is not visible on the timescale of the figure) to x(t) ≈ 500. This corresponds to the number of monomers x0=λ/d which provides the initial exponential growth. According to a complicated dynamics it eventually approaches its steady-state value xst= given by Eq. 38 (dashed line). The parameters are n=6, a=0.05, b=9×10−4, β=0.015, λ=200,000, and d=400.
Biophysical Journal  , DOI: ( /S (03) )
Copyright © 2003 The Biophysical Society Terms and Conditions

9. Figure 8
Evolution of the average size of PrPsc polymers s=z(t)/y(t). The simulation starts with s(0)=200. The dashed line shows the analytical result, Eq. 37. The parameters are given in the caption of Fig. 7.
Biophysical Journal  , DOI: ( /S (03) )
Copyright © 2003 The Biophysical Society Terms and Conditions

10. Figure 9
Evolution of the number of PrPsc polymers y(t) (left) and the total mass of polymers z(t). For comparison, the dashed lines show the solution of the simplified set of equations, Eq. 14, with the exponents and coefficients given by Eqs. 16 and 17, respectively, with x0=λ/d. The parameters of the simulation are given in the caption of Fig. 7.
Biophysical Journal  , DOI: ( /S (03) )
Copyright © 2003 The Biophysical Society Terms and Conditions

11. Figure 10
Size distributions of PrPsc polymers for the full model, including x=x(t). The points display numerical simulations and the line shows the analytical result, Eq. 39. The parameters of the simulation are given in the caption of Fig. 7. For comparison, the dashed line shows the result for the simplified model with x(t)=λ/d=const. due to Eq. 26.
Biophysical Journal  , DOI: ( /S (03) )
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12. Figure 11
Evolution of the size distribution for the initial condition y50(0)=435, yi(0)=0 for i≠50. The parameters of the simulation are given in the caption of Fig. 7.
Biophysical Journal  , DOI: ( /S (03) )
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13. Figure 12
Influence of the size distribution of the inoculation to the evolution of the distribution. The parameters are n=6, d=100, a=0.027, b=0.0048, λ=106, and β= For explanation, see text.
Biophysical Journal  , DOI: ( /S (03) )
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14. Figure 13
Total mass of PrPsc molecules, z(t) over time for different initial size distributions as shown in Fig. 12. The initial total mass, z(0)=16,000, is identical in all cases. The full line corresponds to the left plot in Fig. 12, the dashed line to the middle plot, and the dotted line to the filtered inoculation drawn in the right plot.
Biophysical Journal  , DOI: ( /S (03) )
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15. Figure 14
The incubation time is sensitive to the size distribution of the inoculation. The figure shows the model incubation time over the level of filtering as defined by Eq. 41 for an identical number of PrPsc units in the inoculation, i.e., for the same value of z(0).
Biophysical Journal  , DOI: ( /S (03) )
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16. Figure 15
Time-dependent number of PrPsc polymers as it follows from the numerical simulation of the set of equations in Eq. 11, including the time-dependence of the number of monomers (full line) together with the experimental data (points) (Rubenstein et al., 1991). The abundance of the fibrils (given in this reference as a number of PrPsc per a square element of the substrate) was obtained by negative-stain electron microscopy at various times after intracerebral inoculation. The measurements were performed for the spleens of Compton white mice and C57BL/6j mice. The dashed line show the prediction of the simplified model with the same rate constants but with a constant number of monomers, x0=λ/d; see Eq. 13. The parameters are n=6, a=0.027, b=4.8×10−4, β=0.8, λ=1080, and d=215.
Biophysical Journal  , DOI: ( /S (03) )
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17. Figure 16
The same as Fig. 15, but for the intraperitoneal inoculation. The parameters are n=6, a=0.018, b=3.2×10−4, β=0.32, λ=1170, and d=140.
Biophysical Journal  , DOI: ( /S (03) )
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18. Figure 17
To choose randomly the transition μ by which the system escapes from the present state S→ we set up an array V containing the cumulative rates, i.e., V[0]=0, V[1]=V[0]+A1=V[0]+λ, V[2]=V[1]+A2=V[1]+dx, V[3]=V[2]+A3=V[3]+ayn, etc. Then we draw an equidistributed random number RND from the interval [0,∑Ai]. The process i for which V[i−1]<RND≤V[i] is chosen to be the next process.
Biophysical Journal  , DOI: ( /S (03) )
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