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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

Qualitative agreement between mean-field and 3D models.(a) In a model with activation (kA=1) and no polymer fragmentation or latentization (kf=kL=0), the weighted mean polymer size mw=M2/M1 exhibits a transition from growth as t3 to linear scaling in t. Here we have plotted against time rescaled by activation rate, kAt. (b) For fixed kA, time series for different kP values can be collapsed by rescaling mw−1 by kp. (c) Allowing polymer fragmentation limits the growth of polymers. Here the activation rate is kA=1, the polymerization rate kp=1, and there is no latentization (kL=0), and the growth in unweighted mean size of polymers of length i≥2,  has been plotted. (d) Latentization slows polymer growth, as seen here for the weighted mean polymer size mw. Activation is not incorporated here, and no fragmentation occurs (kf=0), and kp=1. We plot against time rescaled by kp. When fragmentation is allowed, the system always attains a steady state in which all mass consists of latent monomers. Analogous plots for the 3D model are shown in Fig. 2.
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f3: Qualitative agreement between mean-field and 3D models.(a) In a model with activation (kA=1) and no polymer fragmentation or latentization (kf=kL=0), the weighted mean polymer size mw=M2/M1 exhibits a transition from growth as t3 to linear scaling in t. Here we have plotted against time rescaled by activation rate, kAt. (b) For fixed kA, time series for different kP values can be collapsed by rescaling mw−1 by kp. (c) Allowing polymer fragmentation limits the growth of polymers. Here the activation rate is kA=1, the polymerization rate kp=1, and there is no latentization (kL=0), and the growth in unweighted mean size of polymers of length i≥2, has been plotted. (d) Latentization slows polymer growth, as seen here for the weighted mean polymer size mw. Activation is not incorporated here, and no fragmentation occurs (kf=0), and kp=1. We plot against time rescaled by kp. When fragmentation is allowed, the system always attains a steady state in which all mass consists of latent monomers. Analogous plots for the 3D model are shown in Fig. 2.

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)

Qualitative agreement between mean-field and 3D models.(a) In a model with activation (kA=1) and no polymer fragmentation or latentization (kf=kL=0), the weighted mean polymer size mw=M2/M1 exhibits a transition from growth as t3 to linear scaling in t. Here we have plotted against time rescaled by activation rate, kAt. (b) For fixed kA, time series for different kP values can be collapsed by rescaling mw−1 by kp. (c) Allowing polymer fragmentation limits the growth of polymers. Here the activation rate is kA=1, the polymerization rate kp=1, and there is no latentization (kL=0), and the growth in unweighted mean size of polymers of length i≥2,  has been plotted. (d) Latentization slows polymer growth, as seen here for the weighted mean polymer size mw. Activation is not incorporated here, and no fragmentation occurs (kf=0), and kp=1. We plot against time rescaled by kp. When fragmentation is allowed, the system always attains a steady state in which all mass consists of latent monomers. Analogous plots for the 3D model are shown in Fig. 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Qualitative agreement between mean-field and 3D models.(a) In a model with activation (kA=1) and no polymer fragmentation or latentization (kf=kL=0), the weighted mean polymer size mw=M2/M1 exhibits a transition from growth as t3 to linear scaling in t. Here we have plotted against time rescaled by activation rate, kAt. (b) For fixed kA, time series for different kP values can be collapsed by rescaling mw−1 by kp. (c) Allowing polymer fragmentation limits the growth of polymers. Here the activation rate is kA=1, the polymerization rate kp=1, and there is no latentization (kL=0), and the growth in unweighted mean size of polymers of length i≥2, has been plotted. (d) Latentization slows polymer growth, as seen here for the weighted mean polymer size mw. Activation is not incorporated here, and no fragmentation occurs (kf=0), and kp=1. We plot against time rescaled by kp. When fragmentation is allowed, the system always attains a steady state in which all mass consists of latent monomers. Analogous plots for the 3D model are shown in Fig. 2.
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