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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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Polymerization kinetics in vitro is controlled by protein concentration.When proteins cannot enter or exit the system, the concentration is constant and controls the kinetics. (a) We report the average weighted mass as a function of time for different concentrations for kf=0 and kL=0. The curves show a crossover between two power laws and can be fitted as discussed in the main text. (b) All the curves from (a) can be collapsed into a single master curve when variables are properly rescaled by the concentration. This implies that the crossover timescales as a power law of the concentration as shown in the inset. (c) If we use a non-vanishing rate of polymer fragmentation (kf>0), the growth is limited. (d) Latentization (kL>0) leads to slowing down of the growth, which at long times resumes as in the case kL=0. This behaviour has been experimentally observed in vitro for neuroserpin, as shown in the inset (data from ref. 34). Curves are obtained by averaging over 10 realizations obtained from statistically identical initial conditions.
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f2: Polymerization kinetics in vitro is controlled by protein concentration.When proteins cannot enter or exit the system, the concentration is constant and controls the kinetics. (a) We report the average weighted mass as a function of time for different concentrations for kf=0 and kL=0. The curves show a crossover between two power laws and can be fitted as discussed in the main text. (b) All the curves from (a) can be collapsed into a single master curve when variables are properly rescaled by the concentration. This implies that the crossover timescales as a power law of the concentration as shown in the inset. (c) If we use a non-vanishing rate of polymer fragmentation (kf>0), the growth is limited. (d) Latentization (kL>0) leads to slowing down of the growth, which at long times resumes as in the case kL=0. This behaviour has been experimentally observed in vitro for neuroserpin, as shown in the inset (data from ref. 34). Curves are obtained by averaging over 10 realizations obtained from statistically identical initial conditions.

Mentions: We start the simulations from a fixed number Nm of inactive monomers, randomly distributed in space, and then study the effect of different concentrations, measured by the dimensionless density . We quantify the aggregation kinetics by measuring the weighted polymer mass mw=‹i2›/‹i›, where i is the number of monomers in each polymer and the average is taken over different realizations of the process. This observable is accessible experimentally through dynamic light scattering34. Figure 2a shows that for kf=0 the weighted mass kinetics displays a crossover between a short-time regime growing as t2, owing to activation and dimerization (Supplementary Fig. 1), and a long-time regime growing as tβ with β≃0.5, owing to polymer–polymer aggregation. The results are in agreement with experiments34. We fit the curves obtained at different densities to a crossover function (see Supplementary Information) depending on a crossover time τ scaling as ρ−γ (see the inset of Fig. 2b). The best fit yields γ=0.149±0.002 and allows rescaling of all the curves onto a single master curve. This result confirms that the concentration only sets the timescale of the kinetics. In Fig. 2c, we study the effect of polymer fragmentation showing that if kf>0 the polymerization process is blocked after a characteristic time that depends on kf. The role of latentization is illustrated in Fig. 2d, which shows that the long-time growth is not affected if kL>0. Latentization induces a plateau in the crossover region, a feature that is also observed in experiments (see the inset of Fig. 2d and ref. 34). Mean-field theory can also be used to study polymerization kinetics in vitro, and yields qualitative agreement with the 3D model, albeit with quantitative differences, as shown in Fig. 3. However, the two models agree on essential features.


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 vitro is controlled by protein concentration.When proteins cannot enter or exit the system, the concentration is constant and controls the kinetics. (a) We report the average weighted mass as a function of time for different concentrations for kf=0 and kL=0. The curves show a crossover between two power laws and can be fitted as discussed in the main text. (b) All the curves from (a) can be collapsed into a single master curve when variables are properly rescaled by the concentration. This implies that the crossover timescales as a power law of the concentration as shown in the inset. (c) If we use a non-vanishing rate of polymer fragmentation (kf>0), the growth is limited. (d) Latentization (kL>0) leads to slowing down of the growth, which at long times resumes as in the case kL=0. This behaviour has been experimentally observed in vitro for neuroserpin, as shown in the inset (data from ref. 34). Curves are obtained by averaging over 10 realizations obtained from statistically identical initial conditions.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Polymerization kinetics in vitro is controlled by protein concentration.When proteins cannot enter or exit the system, the concentration is constant and controls the kinetics. (a) We report the average weighted mass as a function of time for different concentrations for kf=0 and kL=0. The curves show a crossover between two power laws and can be fitted as discussed in the main text. (b) All the curves from (a) can be collapsed into a single master curve when variables are properly rescaled by the concentration. This implies that the crossover timescales as a power law of the concentration as shown in the inset. (c) If we use a non-vanishing rate of polymer fragmentation (kf>0), the growth is limited. (d) Latentization (kL>0) leads to slowing down of the growth, which at long times resumes as in the case kL=0. This behaviour has been experimentally observed in vitro for neuroserpin, as shown in the inset (data from ref. 34). Curves are obtained by averaging over 10 realizations obtained from statistically identical initial conditions.
Mentions: We start the simulations from a fixed number Nm of inactive monomers, randomly distributed in space, and then study the effect of different concentrations, measured by the dimensionless density . We quantify the aggregation kinetics by measuring the weighted polymer mass mw=‹i2›/‹i›, where i is the number of monomers in each polymer and the average is taken over different realizations of the process. This observable is accessible experimentally through dynamic light scattering34. Figure 2a shows that for kf=0 the weighted mass kinetics displays a crossover between a short-time regime growing as t2, owing to activation and dimerization (Supplementary Fig. 1), and a long-time regime growing as tβ with β≃0.5, owing to polymer–polymer aggregation. The results are in agreement with experiments34. We fit the curves obtained at different densities to a crossover function (see Supplementary Information) depending on a crossover time τ scaling as ρ−γ (see the inset of Fig. 2b). The best fit yields γ=0.149±0.002 and allows rescaling of all the curves onto a single master curve. This result confirms that the concentration only sets the timescale of the kinetics. In Fig. 2c, we study the effect of polymer fragmentation showing that if kf>0 the polymerization process is blocked after a characteristic time that depends on kf. The role of latentization is illustrated in Fig. 2d, which shows that the long-time growth is not affected if kL>0. Latentization induces a plateau in the crossover region, a feature that is also observed in experiments (see the inset of Fig. 2d and ref. 34). Mean-field theory can also be used to study polymerization kinetics in vitro, and yields qualitative agreement with the 3D model, albeit with quantitative differences, as shown in Fig. 3. However, the two models agree on essential features.

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