Kinetics and Thermodynamics of Fluctuation‐Induced Transitions in Multistable Systems

Nicolis, Grégoire; Nicolis, C.

doi:10.1002/9781118309513.ch1

Cited by 3 publications

(2 citation statements)

References 38 publications

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“…Its inverse defines the lifetime of the decaying state, which represents an intrinsic property of the system. This paradigm is fundamental to nucleation theory and reaction-rate theory in chemistry, physics, and biology [1]- [6].…”

Section: Introductionmentioning

confidence: 99%

A trace formula for activated escape in noisy maps

Demaeyer¹,

Gaspard²

2013

J. Stat. Mech.

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Using path-integral methods, a formula is deduced for the noise-induced escape rate from an attracting fixed point across an unstable fixed point in one-dimensional maps. The calculation starts from the trace formula for the eigenvalues of the Frobenius-Perron operator ruling the time evolution of the probability density in noisy maps. The escape rate is determined from the loop formed by two heteroclinic orbits connecting back and forth the two fixed points of the one-dimensional map extended to a two-dimensional symplectic map. The escape rate is obtained with the expression of the prefactor to Arrhenius-van't Hoff exponential factor.

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Section: Introductionmentioning

confidence: 99%

A trace formula for activated escape in noisy maps

Demaeyer¹,

Gaspard²

2013

J. Stat. Mech.

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“…One of the assumptions of the CNT is that all clusters exhibit the same crystallinity degree regardless of their size . However, the validity of some of these assumptions has been questioned and even contradicted over the past 2 decades by different theories/observations, which can be resumed as follows. − Experimental observations : when the nucleation rate is much faster or slower than the one predicted by the CNT or when the observed nuclei size distribution differs significantly from the theoretical predictions. Thermodynamic calculations : when the thermodynamic calculations (e.g., free energy barrier) are much different compared to the values predicted by the CNT or when the critical nucleus size significantly differs from the estimated value. Nonclassical nucleation theories : when the existence of nonclassical nucleation pathways that do not involve the formation of a critical nucleus, which might suggest that the CNT does not fully describe the nucleation process. …”

Section: Introductionmentioning

confidence: 99%

Classical and Nonclassical Nucleation Mechanisms of Insulin Crystals

Ferreira,

Domínguez-Arca,

Carneiro

et al. 2024

ACS Omega

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Although the Classical Nucleation Theory (CNT) is the most consensual theory to explain protein nucleation mechanisms, experimental observations during the shear-induced assays suggest that the CNT does not always describe the insulin nucleation process. This is the case at intermediate precipitant (ZnCl2) solution concentrations (2.3 mM) and high-temperature values (20 and 40 °C) as well as at low precipitant solution concentrations (1.6 mM) and low-temperature values (5 °C). In this work, crystallization events following the CNT registered at high precipitant solution concentrations (3.1 and 4.7 mM) are typically described by a Newtonian response. On the other hand, crystallization events following a nonclassical nucleation pathway seem to involve the formation of a metastable intermediate state before crystal formation and are described by a transition from Newtonian to shear-thinning responses. A dominant shear-thinning behavior (shear viscosity values ranging more than 6 orders of magnitude) is found during aggregation/agglomeration events. The rheological analysis is complemented with different characterization techniques (Dynamic Light Scattering, Energy-Dispersive Spectroscopy, Circular Dichroism, and Differential Scanning Calorimetry) to understand the insulin behavior in solution, especially during the occurrence of aggregation/agglomeration events. To the best of our knowledge, the current work is the first study describing nonclassical nucleation mechanisms during shear-induced crystallization experiments, which reveals the potential of the interdisciplinary approach herein described and opens a window for a clear understanding of protein nucleation mechanisms.

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Stochastic resonance in multistable systems: The role of dimensionality

Nicolis

2012

Phys. Rev. E

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The theory of stochastic resonance in multistable systems is extended to account for both direct transitions between all stable states present and indirect ones involving intermediate states. It is shown that to satisfy these requirements the dynamics needs to be embedded in phase spaces of dimension equal to at least two. Under well defined conditions, the conjunction of the presence of intermediate states and the multidimensional character of the process leads to an enhancement of the response of the system to an external periodic forcing.

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Kinetics and Thermodynamics of Fluctuation‐Induced Transitions in Multistable Systems

Cited by 3 publications

References 38 publications

A trace formula for activated escape in noisy maps

A trace formula for activated escape in noisy maps

Classical and Nonclassical Nucleation Mechanisms of Insulin Crystals

Stochastic resonance in multistable systems: The role of dimensionality

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