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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.

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Related in: MedlinePlus

Polymerization kinetics in vivo displays a non-equilibrium phase transition.In the ER proteins, enter and exit the system and concentration is not constant. (a) Mean-field calculations of the average polymer length for different rate of polymer exit kout grows diffusively as . Above a critical value , which depends on the other rate parameters, growth eventually stops, while it persists for . (b) The prefactor C goes to zero at the transition according to a power law with exponent θ=1/2. (c) The average polymer length obtained from 3D numerical simulations grows similar to mean-field theory with a transition at . Curves are obtained by averaging over 200–1000 realizations, depending on the proximity to the critical point. (d) The prefactor C in three dimensions goes also to zero at the transition but the curve is not sharp, probably because of finite size effects.
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f4: Polymerization kinetics in vivo displays a non-equilibrium phase transition.In the ER proteins, enter and exit the system and concentration is not constant. (a) Mean-field calculations of the average polymer length for different rate of polymer exit kout grows diffusively as . Above a critical value , which depends on the other rate parameters, growth eventually stops, while it persists for . (b) The prefactor C goes to zero at the transition according to a power law with exponent θ=1/2. (c) The average polymer length obtained from 3D numerical simulations grows similar to mean-field theory with a transition at . Curves are obtained by averaging over 200–1000 realizations, depending on the proximity to the critical point. (d) The prefactor C in three dimensions goes also to zero at the transition but the curve is not sharp, probably because of finite size effects.

Mentions: To describe in vivo conditions, we introduce to our models non-zero rates for protein synthesis (kin) and degradation (kout). These effects are in competition: protein synthesis allows greater polymer growth via a flux of monomers that combine into larger polymers; however this growth can be balanced by polymer degradation. To study this quantitatively, we turn first to the mean-field model. Here we characterize polymer aggregation by the mean length mp of polymers of size i≥2, which is given by the ratio of the mass and the number of polymers, . As discussed above, when protein synthesis and degradation are turned off, as in experiments performed in vitro, the mean-field model predicts a finite steady state mean polymer size26. However, if protein synthesis is turned on, with rate kin, then if kout is small, the mean polymer size increases as Ctβ, with β=0.5. On the other hand, if kout is greater than a critical value , which depends on the rates of aggregation and fragmentation, a non-growing steady state is again obtained (Fig. 4a and Supplementary Fig. 2 and 3). As shown in Fig. 4b, we find a sharp transition between growing and stationary phases as quantified by the prefactor of the square-root growth of the mean polymer size C, which scales to zero as , with θ=1/2, when the transition is approached.


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

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

Polymerization kinetics in vivo displays a non-equilibrium phase transition.In the ER proteins, enter and exit the system and concentration is not constant. (a) Mean-field calculations of the average polymer length for different rate of polymer exit kout grows diffusively as . Above a critical value , which depends on the other rate parameters, growth eventually stops, while it persists for . (b) The prefactor C goes to zero at the transition according to a power law with exponent θ=1/2. (c) The average polymer length obtained from 3D numerical simulations grows similar to mean-field theory with a transition at . Curves are obtained by averaging over 200–1000 realizations, depending on the proximity to the critical point. (d) The prefactor C in three dimensions goes also to zero at the transition but the curve is not sharp, probably because of finite size effects.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Polymerization kinetics in vivo displays a non-equilibrium phase transition.In the ER proteins, enter and exit the system and concentration is not constant. (a) Mean-field calculations of the average polymer length for different rate of polymer exit kout grows diffusively as . Above a critical value , which depends on the other rate parameters, growth eventually stops, while it persists for . (b) The prefactor C goes to zero at the transition according to a power law with exponent θ=1/2. (c) The average polymer length obtained from 3D numerical simulations grows similar to mean-field theory with a transition at . Curves are obtained by averaging over 200–1000 realizations, depending on the proximity to the critical point. (d) The prefactor C in three dimensions goes also to zero at the transition but the curve is not sharp, probably because of finite size effects.
Mentions: To describe in vivo conditions, we introduce to our models non-zero rates for protein synthesis (kin) and degradation (kout). These effects are in competition: protein synthesis allows greater polymer growth via a flux of monomers that combine into larger polymers; however this growth can be balanced by polymer degradation. To study this quantitatively, we turn first to the mean-field model. Here we characterize polymer aggregation by the mean length mp of polymers of size i≥2, which is given by the ratio of the mass and the number of polymers, . As discussed above, when protein synthesis and degradation are turned off, as in experiments performed in vitro, the mean-field model predicts a finite steady state mean polymer size26. However, if protein synthesis is turned on, with rate kin, then if kout is small, the mean polymer size increases as Ctβ, with β=0.5. On the other hand, if kout is greater than a critical value , which depends on the rates of aggregation and fragmentation, a non-growing steady state is again obtained (Fig. 4a and Supplementary Fig. 2 and 3). As shown in Fig. 4b, we find a sharp transition between growing and stationary phases as quantified by the prefactor of the square-root growth of the mean polymer size C, which scales to zero as , with θ=1/2, when the transition is approached.

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