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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

Phase transition affects protein clearance from the central nervous system.Evolution of the measured protein clearance as the physiological–pathological phase transition is approached, simulated in the mean-field model and compared with experimental data. (a) Ratio of labelled to unlabelled protein in the cerebrospinal fluid at different values of the control parameter kout (measured in s−1). After each measurement, kout is decreased and the system evolves for 3 years to reach a new steady state, as described in the Supplementary Information. Parameter values are chosen so the first labelling measurement agrees with experimental data (shown as black dots), which are taken from Fig. 3c in ref. 37. (b) Measured fractional clearance rate (FCR), defined as the slope of the log of the labelled/unlabelled ratio in the period 30–36 h. FCR decreases with kout, and near the critical value of kout (here kout=0.03125, s−1, indicated by the dashed line), no clearance would be measured before t=36 h.
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f9: Phase transition affects protein clearance from the central nervous system.Evolution of the measured protein clearance as the physiological–pathological phase transition is approached, simulated in the mean-field model and compared with experimental data. (a) Ratio of labelled to unlabelled protein in the cerebrospinal fluid at different values of the control parameter kout (measured in s−1). After each measurement, kout is decreased and the system evolves for 3 years to reach a new steady state, as described in the Supplementary Information. Parameter values are chosen so the first labelling measurement agrees with experimental data (shown as black dots), which are taken from Fig. 3c in ref. 37. (b) Measured fractional clearance rate (FCR), defined as the slope of the log of the labelled/unlabelled ratio in the period 30–36 h. FCR decreases with kout, and near the critical value of kout (here kout=0.03125, s−1, indicated by the dashed line), no clearance would be measured before t=36 h.

Mentions: Measured FCRs depend on many parameters (see Supplementary Table 1) but here we focus on the role of protein degradation, controlled by kout. A single FCR measurement does not allow a determination of all parameters, but our results indicate that a series of labelling experiments can reveal changes in degradation rates over time and the approach to the physiological–pathological phase transition. We take the steady-state system and decrease kout slightly, and allow it to evolve a further 3 years to attain a new steady state, after which we perform another labelling test. As reported in Fig. 9b, a reduced kout yields a reduction in FCR, as well as the maximum labelled/unlabelled ratio. Further decreases in kout cause measured FCR to continue to decrease, but as the critical point is approached the lifetime of labelled proteins diverges and near the critical point no clearance is observed in experimental timescales. Further experiments by the same group indeed reveal that FCR decreases for AD patients with mild symptoms38, in agreement with the predictions of our model.


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

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

Phase transition affects protein clearance from the central nervous system.Evolution of the measured protein clearance as the physiological–pathological phase transition is approached, simulated in the mean-field model and compared with experimental data. (a) Ratio of labelled to unlabelled protein in the cerebrospinal fluid at different values of the control parameter kout (measured in s−1). After each measurement, kout is decreased and the system evolves for 3 years to reach a new steady state, as described in the Supplementary Information. Parameter values are chosen so the first labelling measurement agrees with experimental data (shown as black dots), which are taken from Fig. 3c in ref. 37. (b) Measured fractional clearance rate (FCR), defined as the slope of the log of the labelled/unlabelled ratio in the period 30–36 h. FCR decreases with kout, and near the critical value of kout (here kout=0.03125, s−1, indicated by the dashed line), no clearance would be measured before t=36 h.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f9: Phase transition affects protein clearance from the central nervous system.Evolution of the measured protein clearance as the physiological–pathological phase transition is approached, simulated in the mean-field model and compared with experimental data. (a) Ratio of labelled to unlabelled protein in the cerebrospinal fluid at different values of the control parameter kout (measured in s−1). After each measurement, kout is decreased and the system evolves for 3 years to reach a new steady state, as described in the Supplementary Information. Parameter values are chosen so the first labelling measurement agrees with experimental data (shown as black dots), which are taken from Fig. 3c in ref. 37. (b) Measured fractional clearance rate (FCR), defined as the slope of the log of the labelled/unlabelled ratio in the period 30–36 h. FCR decreases with kout, and near the critical value of kout (here kout=0.03125, s−1, indicated by the dashed line), no clearance would be measured before t=36 h.
Mentions: Measured FCRs depend on many parameters (see Supplementary Table 1) but here we focus on the role of protein degradation, controlled by kout. A single FCR measurement does not allow a determination of all parameters, but our results indicate that a series of labelling experiments can reveal changes in degradation rates over time and the approach to the physiological–pathological phase transition. We take the steady-state system and decrease kout slightly, and allow it to evolve a further 3 years to attain a new steady state, after which we perform another labelling test. As reported in Fig. 9b, a reduced kout yields a reduction in FCR, as well as the maximum labelled/unlabelled ratio. Further decreases in kout cause measured FCR to continue to decrease, but as the critical point is approached the lifetime of labelled proteins diverges and near the critical point no clearance is observed in experimental timescales. Further experiments by the same group indeed reveal that FCR decreases for AD patients with mild symptoms38, in agreement with the predictions of our model.

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