Limits...
Protein accumulation in the endoplasmic reticulum as a non-equilibrium phase transition.

Budrikis Z, Costantini G, La Porta CA, Zapperi S - Nat Commun (2014)

Bottom Line: Here we study protein aggregation kinetics by mean-field reactions and three dimensional Monte carlo simulations of diffusion-limited aggregation of linear polymers in a confined space, representing the endoplasmic reticulum.By tuning the rates of protein production and degradation, we show that the system undergoes a non-equilibrium phase transition from a physiological phase with little or no polymer accumulation to a pathological phase characterized by persistent polymerization.The model can be successfully used to interpret experimental data on amyloid-β clearance from the central nervous system.

View Article: PubMed Central - PubMed

Affiliation: Institute for Scientific Interchange Foundation, Via Alassio 11/C, Torino 10126, Italy.

ABSTRACT
Several neurological disorders are associated with the aggregation of aberrant proteins, often localized in intracellular organelles such as the endoplasmic reticulum. Here we study protein aggregation kinetics by mean-field reactions and three dimensional Monte carlo simulations of diffusion-limited aggregation of linear polymers in a confined space, representing the endoplasmic reticulum. By tuning the rates of protein production and degradation, we show that the system undergoes a non-equilibrium phase transition from a physiological phase with little or no polymer accumulation to a pathological phase characterized by persistent polymerization. A combination of external factors accumulating during the lifetime of a patient can thus slightly modify the phase transition control parameters, tipping the balance from a long symptomless lag phase to an accelerated pathological development. The model can be successfully used to interpret experimental data on amyloid-β clearance from the central nervous system.

Show MeSH

Related in: MedlinePlus

Mean-field phase diagram.Phase diagram of the mean-field model. The manifold in parameter space separates those parameters for which a steady state is obtained (the stationary phase) and those that lead to continual growth of polymers (the growing phase). The model used here has a polymer degradation rate that scales with polymer size i as i−3, up to a cutoff c=5, but similar phase diagrams are obtained for different size dependences and cutoffs and in much of the phase space the location of the transition is predicted well by a model with c=1, as discussed in the Supplementary Information.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4048836&req=5

f5: Mean-field phase diagram.Phase diagram of the mean-field model. The manifold in parameter space separates those parameters for which a steady state is obtained (the stationary phase) and those that lead to continual growth of polymers (the growing phase). The model used here has a polymer degradation rate that scales with polymer size i as i−3, up to a cutoff c=5, but similar phase diagrams are obtained for different size dependences and cutoffs and in much of the phase space the location of the transition is predicted well by a model with c=1, as discussed in the Supplementary Information.

Mentions: Figure 5 shows the phase diagram estimated by the mean-field model as a function of the rates kin, kout, kf and kp. The transition region is governed by the products kinkp and koutkf. Intuitively, kinkp controls the rate of polymer growth, by the introduction of new monomers and their aggregation into larger polymers, while koutkf controls the rate of polymer shortening by the removal of material and fragmentation of large polymers. When kf is large relative to kinkp, the dependence on parameters is further reduced to a dependence on the ratio kinkp/koutkf. Indeed, in the limit c=1, it can be shown that if a steady state exists, the relationship (kinkp)/(2koutkf)+(kin/kout)(1/M0)=1 must be satisfied, where . This relation determines the location of the critical region as discussed in detail in the Supplementary Information.


Protein accumulation in the endoplasmic reticulum as a non-equilibrium phase transition.

Budrikis Z, Costantini G, La Porta CA, Zapperi S - Nat Commun (2014)

Mean-field phase diagram.Phase diagram of the mean-field model. The manifold in parameter space separates those parameters for which a steady state is obtained (the stationary phase) and those that lead to continual growth of polymers (the growing phase). The model used here has a polymer degradation rate that scales with polymer size i as i−3, up to a cutoff c=5, but similar phase diagrams are obtained for different size dependences and cutoffs and in much of the phase space the location of the transition is predicted well by a model with c=1, as discussed in the Supplementary Information.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4048836&req=5

f5: Mean-field phase diagram.Phase diagram of the mean-field model. The manifold in parameter space separates those parameters for which a steady state is obtained (the stationary phase) and those that lead to continual growth of polymers (the growing phase). The model used here has a polymer degradation rate that scales with polymer size i as i−3, up to a cutoff c=5, but similar phase diagrams are obtained for different size dependences and cutoffs and in much of the phase space the location of the transition is predicted well by a model with c=1, as discussed in the Supplementary Information.
Mentions: Figure 5 shows the phase diagram estimated by the mean-field model as a function of the rates kin, kout, kf and kp. The transition region is governed by the products kinkp and koutkf. Intuitively, kinkp controls the rate of polymer growth, by the introduction of new monomers and their aggregation into larger polymers, while koutkf controls the rate of polymer shortening by the removal of material and fragmentation of large polymers. When kf is large relative to kinkp, the dependence on parameters is further reduced to a dependence on the ratio kinkp/koutkf. Indeed, in the limit c=1, it can be shown that if a steady state exists, the relationship (kinkp)/(2koutkf)+(kin/kout)(1/M0)=1 must be satisfied, where . This relation determines the location of the critical region as discussed in detail in the Supplementary Information.

Bottom Line: Here we study protein aggregation kinetics by mean-field reactions and three dimensional Monte carlo simulations of diffusion-limited aggregation of linear polymers in a confined space, representing the endoplasmic reticulum.By tuning the rates of protein production and degradation, we show that the system undergoes a non-equilibrium phase transition from a physiological phase with little or no polymer accumulation to a pathological phase characterized by persistent polymerization.The model can be successfully used to interpret experimental data on amyloid-β clearance from the central nervous system.

View Article: PubMed Central - PubMed

Affiliation: Institute for Scientific Interchange Foundation, Via Alassio 11/C, Torino 10126, Italy.

ABSTRACT
Several neurological disorders are associated with the aggregation of aberrant proteins, often localized in intracellular organelles such as the endoplasmic reticulum. Here we study protein aggregation kinetics by mean-field reactions and three dimensional Monte carlo simulations of diffusion-limited aggregation of linear polymers in a confined space, representing the endoplasmic reticulum. By tuning the rates of protein production and degradation, we show that the system undergoes a non-equilibrium phase transition from a physiological phase with little or no polymer accumulation to a pathological phase characterized by persistent polymerization. A combination of external factors accumulating during the lifetime of a patient can thus slightly modify the phase transition control parameters, tipping the balance from a long symptomless lag phase to an accelerated pathological development. The model can be successfully used to interpret experimental data on amyloid-β clearance from the central nervous system.

Show MeSH
Related in: MedlinePlus