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Investigating the conformational stability of prion strains through a kinetic replication model.

Zampieri M, Legname G, Altafini C - PLoS Comput. Biol. (2009)

Bottom Line: The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage.A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows).The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils' mean length) and is coherent with all experimental observations concerning strain-specific behavior.

View Article: PubMed Central - PubMed

Affiliation: Functional Analysis Sector, International School for Advanced Studies, Trieste, Italy.

ABSTRACT
Prion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrP(Sc) structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils' mean length) and is coherent with all experimental observations concerning strain-specific behavior.

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Related in: MedlinePlus

Relationships between ,  and .In (A) and (B) the stability against denaturation is plotted against the reproductive ratio and the rate of growth. A direct proportionality links  to . As expected, an inverse proportionality emerges between  and , reinforcing the previous results.
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pcbi-1000420-g002: Relationships between , and .In (A) and (B) the stability against denaturation is plotted against the reproductive ratio and the rate of growth. A direct proportionality links to . As expected, an inverse proportionality emerges between and , reinforcing the previous results.

Mentions: From these simplified formulas it is clear that an increase in the frangibility of the fibers (i.e., in ) produces an increment of (Eq. 7) and a decrement of (Eq. 8) in agreement with the trend in Figure 1. Therefore, from the model we expect to give the best fitting result. As a matter of fact, this relationship (black dash-dotted line in Figure 1) does not provide the optimal fit, although it reproduces the qualitative observed behavior (). The fittings of Figure 1 (see Table 3) suggest that, approximately, (red line) implying that we are observing proportional to and to (see Materials and Methods, Eq. 12). This means that the estimated exponents for are somewhat different from the expected values of () predicted in Eq. 7 and 8. In order to improve the model prediction, we introduce a strain-dependence on a second parameter. The simplest solution suggested by the model for this scope (deducible from Eq. 4 and 5) points to the aggregation rate . By linking to , we are still left with a one-parameter family of models describing the strain-dependence. In doing so, we obtain the estimate (see again Materials and Methods, Eq. 13). This correction yields and , this time respecting the predictions of Eq. 4 and 5. Therefore, on the one hand we can show that at a qualitative level is the only parameter that alone can explain the inverse relationship between and . On the other hand, the variation of by itself is not able to quantitatively describe the experimental data in a precise way. An additional correction, obtained relating to , leads to a substantially improved fitting. Apart from Eq. 4 and 5, our choice of alongside as strain-dependent parameter is suggested by the structure of the model of Eq. 10, in which, of all parameters, those describing the kinetics of fibril aggregation/breakage are the most likely to vary across strains. Both the fitting and the model structure suggest an interplay between and , with partially balancing the effect of .


Investigating the conformational stability of prion strains through a kinetic replication model.

Zampieri M, Legname G, Altafini C - PLoS Comput. Biol. (2009)

Relationships between ,  and .In (A) and (B) the stability against denaturation is plotted against the reproductive ratio and the rate of growth. A direct proportionality links  to . As expected, an inverse proportionality emerges between  and , reinforcing the previous results.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2697384&req=5

pcbi-1000420-g002: Relationships between , and .In (A) and (B) the stability against denaturation is plotted against the reproductive ratio and the rate of growth. A direct proportionality links to . As expected, an inverse proportionality emerges between and , reinforcing the previous results.
Mentions: From these simplified formulas it is clear that an increase in the frangibility of the fibers (i.e., in ) produces an increment of (Eq. 7) and a decrement of (Eq. 8) in agreement with the trend in Figure 1. Therefore, from the model we expect to give the best fitting result. As a matter of fact, this relationship (black dash-dotted line in Figure 1) does not provide the optimal fit, although it reproduces the qualitative observed behavior (). The fittings of Figure 1 (see Table 3) suggest that, approximately, (red line) implying that we are observing proportional to and to (see Materials and Methods, Eq. 12). This means that the estimated exponents for are somewhat different from the expected values of () predicted in Eq. 7 and 8. In order to improve the model prediction, we introduce a strain-dependence on a second parameter. The simplest solution suggested by the model for this scope (deducible from Eq. 4 and 5) points to the aggregation rate . By linking to , we are still left with a one-parameter family of models describing the strain-dependence. In doing so, we obtain the estimate (see again Materials and Methods, Eq. 13). This correction yields and , this time respecting the predictions of Eq. 4 and 5. Therefore, on the one hand we can show that at a qualitative level is the only parameter that alone can explain the inverse relationship between and . On the other hand, the variation of by itself is not able to quantitatively describe the experimental data in a precise way. An additional correction, obtained relating to , leads to a substantially improved fitting. Apart from Eq. 4 and 5, our choice of alongside as strain-dependent parameter is suggested by the structure of the model of Eq. 10, in which, of all parameters, those describing the kinetics of fibril aggregation/breakage are the most likely to vary across strains. Both the fitting and the model structure suggest an interplay between and , with partially balancing the effect of .

Bottom Line: The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage.A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows).The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils' mean length) and is coherent with all experimental observations concerning strain-specific behavior.

View Article: PubMed Central - PubMed

Affiliation: Functional Analysis Sector, International School for Advanced Studies, Trieste, Italy.

ABSTRACT
Prion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrP(Sc) structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils' mean length) and is coherent with all experimental observations concerning strain-specific behavior.

Show MeSH
Related in: MedlinePlus