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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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Relationships between the empirical parameters  and .The reproductive ratio is plotted against the rate of growth. The downward trend is not well described by the linear model with negative angular coefficient () and an intercept () (dotted blue line). In addition, the model prediction with  fixed (dashed-dot black line) fails to precisely represent the data, even if it provides a more reasonable relationship (notice that high stable prions, such as MK4985, would always be associated to positive  values). Introducing one more degree of freedom (exponent ) yields a higher  value (red line, ). This result corresponds to a prediction of . In addition, we tested a further simplified model version (where  is considered to be much smaller than ) according to which  (i.e. , shown in green). Similar conclusions could be drawn.
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pcbi-1000420-g001: Relationships between the empirical parameters and .The reproductive ratio is plotted against the rate of growth. The downward trend is not well described by the linear model with negative angular coefficient () and an intercept () (dotted blue line). In addition, the model prediction with fixed (dashed-dot black line) fails to precisely represent the data, even if it provides a more reasonable relationship (notice that high stable prions, such as MK4985, would always be associated to positive values). Introducing one more degree of freedom (exponent ) yields a higher value (red line, ). This result corresponds to a prediction of . In addition, we tested a further simplified model version (where is considered to be much smaller than ) according to which (i.e. , shown in green). Similar conclusions could be drawn.

Mentions: In order to estimate from experimental measures both parameters ( and ) certain assumptions are necessary (see Materials and Methods for full details). An estimation of and from in vivo experiments and for different prion strains characterized by different values of stability against denaturation () is listed in Table 2. The dataset currently available is limited (as not many prion strains can be fully characterized) and many error sources are potentially affecting the estimation of the parameters. Nevertheless, Figure 1 shows the existence of a negative trend between these two empirical parameters (Pearson correlation = −0.91, p-value = 0.01). If we now turn to the kinetic model and look at the corresponding expressions (Eq. 2, 3) the interesting question is whether such a behavior is predicted by the model itself, and is explainable in terms of some of its parameters, in a way that is both mathematically and biologically plausible. Otherwise stated, we investigate which, if any, among the model parameters best describe the strain variability. The critical size of the nucleus (parameter in the model) plays a marginal role in our analysis and is likely to be a fixed integer, in between 2 and 4, across different strains [23]. Even though it has been argued that a hexamer is the minimum infectious unit [24], it can be shown that the model-based conclusions are not conditioned by the value of . In addition is clearly independent of the prion strains, so we remain with three possible choices: , and . From Eq. 1, increasing means incrementing and this affects and in a similar manner, so that this parameter alone cannot explain the inverse relationship derived in Figure 1. The same can be said for and which, if increased/decreased, would induce changes of equal sign in and . Different conclusions can be drawn when considering as the only strain-varying parameter. This dependence becomes clearer assuming that fibrils cannot be degraded in the exponential phase (, identical results can be obtained supposing that the degradation of the fibrils scales as the fibrils breakage rate, , see Text S2). Such assumption leads to the following expressions:(4)(5)(6)


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

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

Relationships between the empirical parameters  and .The reproductive ratio is plotted against the rate of growth. The downward trend is not well described by the linear model with negative angular coefficient () and an intercept () (dotted blue line). In addition, the model prediction with  fixed (dashed-dot black line) fails to precisely represent the data, even if it provides a more reasonable relationship (notice that high stable prions, such as MK4985, would always be associated to positive  values). Introducing one more degree of freedom (exponent ) yields a higher  value (red line, ). This result corresponds to a prediction of . In addition, we tested a further simplified model version (where  is considered to be much smaller than ) according to which  (i.e. , shown in green). Similar conclusions could be drawn.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000420-g001: Relationships between the empirical parameters and .The reproductive ratio is plotted against the rate of growth. The downward trend is not well described by the linear model with negative angular coefficient () and an intercept () (dotted blue line). In addition, the model prediction with fixed (dashed-dot black line) fails to precisely represent the data, even if it provides a more reasonable relationship (notice that high stable prions, such as MK4985, would always be associated to positive values). Introducing one more degree of freedom (exponent ) yields a higher value (red line, ). This result corresponds to a prediction of . In addition, we tested a further simplified model version (where is considered to be much smaller than ) according to which (i.e. , shown in green). Similar conclusions could be drawn.
Mentions: In order to estimate from experimental measures both parameters ( and ) certain assumptions are necessary (see Materials and Methods for full details). An estimation of and from in vivo experiments and for different prion strains characterized by different values of stability against denaturation () is listed in Table 2. The dataset currently available is limited (as not many prion strains can be fully characterized) and many error sources are potentially affecting the estimation of the parameters. Nevertheless, Figure 1 shows the existence of a negative trend between these two empirical parameters (Pearson correlation = −0.91, p-value = 0.01). If we now turn to the kinetic model and look at the corresponding expressions (Eq. 2, 3) the interesting question is whether such a behavior is predicted by the model itself, and is explainable in terms of some of its parameters, in a way that is both mathematically and biologically plausible. Otherwise stated, we investigate which, if any, among the model parameters best describe the strain variability. The critical size of the nucleus (parameter in the model) plays a marginal role in our analysis and is likely to be a fixed integer, in between 2 and 4, across different strains [23]. Even though it has been argued that a hexamer is the minimum infectious unit [24], it can be shown that the model-based conclusions are not conditioned by the value of . In addition is clearly independent of the prion strains, so we remain with three possible choices: , and . From Eq. 1, increasing means incrementing and this affects and in a similar manner, so that this parameter alone cannot explain the inverse relationship derived in Figure 1. The same can be said for and which, if increased/decreased, would induce changes of equal sign in and . Different conclusions can be drawn when considering as the only strain-varying parameter. This dependence becomes clearer assuming that fibrils cannot be degraded in the exponential phase (, identical results can be obtained supposing that the degradation of the fibrils scales as the fibrils breakage rate, , see Text S2). Such assumption leads to the following expressions:(4)(5)(6)

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