Stepping molecular motor amid Lévy white noise

Lisowski, Bartosz; Valenti, Davide; Spagnolo, Bernardo; Bier, Martin; Gudowska–Nowak, Ewa

doi:10.1103/physreve.91.042713

Cited by 93 publications

(38 citation statements)

References 66 publications

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“…In Ref. [40] a numerical study was performed that showed how the mechanics of a processive motor protein gets more complicated if the noise from the bath is Lévy distributed. Above, a more basic and general mechanism has been described analytically.…”

Section: Discussionmentioning

confidence: 99%

Boltzmann-distribution-equivalent for Lévy noise and how it leads to thermodynamically consistent epicatalysis

Bier

2018

Phys. Rev. E

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Nonequilibrium systems commonly exhibit Lévy noise. This means that the distribution for the size of the Brownian fluctuations has a "fat" power-law tail. Large Brownian kicks are then more common as compared to the ordinary Gaussian distribution. We consider a two-state system, i.e., two wells and a barrier in between. The barrier is sufficiently high for a barrier crossing to be a rare event. When the noise is Lévy, we do not get a Boltzmann distribution between the two wells. Instead we get a situation where the distribution between the two wells also depends on the height of the barrier that is in between. Ordinarily, a catalyst, by lowering the barrier between two states, speeds up the relaxation to an equilibrium, but does not change the equilibrium distribution. In an environment with Lévy noise, on the other hand, we have the possibility of epicatalysis, i.e., a catalyst effectively altering the distribution between two states through the changing of the barrier height. After deriving formulas to quantitatively describe this effect, we discuss how this idea may apply in nuclear reactors and in the biochemistry of a living cell.

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Section: Discussionmentioning

confidence: 99%

Boltzmann-distribution-equivalent for Lévy noise and how it leads to thermodynamically consistent epicatalysis

Bier

2018

Phys. Rev. E

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“…In [41], a plot of the interspike intervals and the interevent intervals distributions indicates that neurons and neural network activities are characterized by a non-Gaussian heavy-tail interval distribution, thereby providing a solid reason as to why it makes sense to consider Lévy noise in the study of neural systems. Lévy noise has also been extensively used to model many other complex systems, including lasers [42], quantum dots [43], cardiac dynamics [38], molecular motor [44], economics [45,46], and social systems [47], where changes are often abrupt [48,49]. Furthermore, several studies on stochastic systems have departed from Gaussian to Lévy processes and compared their effects.…”

Section: Introductionmentioning

confidence: 99%

Lévy noise-induced self-induced stochastic resonance in a memristive neuron

Yamakou

Tran

2021

Nonlinear Dyn

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All previous studies on self-induced stochastic resonance (SISR) in neural systems have only considered the idealized Gaussian white noise. Moreover, these studies have ignored one electrophysiological aspect of the nerve cell: its memristive properties. In this paper, first, we show that in the excitable regime, the asymptotic matching of the deterministic timescale and mean escape timescale of an $$\alpha $$ α -stable Lévy process (with value increasing as a power $$\sigma ^{-\alpha }$$ σ - α of the noise amplitude $$\sigma $$ σ , unlike the mean escape timescale of a Gaussian process which increases as in Kramers’ law) can also induce a strong SISR. In addition, it is shown that the degree of SISR induced by Lévy noise is not always higher than that of Gaussian noise. Second, we show that, for both types of noises, the two memristive properties of the neuron have opposite effects on the degree of SISR: the stronger the feedback gain parameter that controls the modulation of the membrane potential with the magnetic flux and the weaker the feedback gain parameter that controls the saturation of the magnetic flux, the higher the degree of SISR. Finally, we show that, for both types of noises, the degree of SISR in the memristive neuron is always higher than in the non-memristive neuron. Our results could guide hardware implementations of neuromorphic silicon circuits operating in noisy regimes.

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“…In [69], a plot of interspike intervals and interevent intervals distributions indicates that neurons and neural network activities are characterized by a non-Gaussian heavy-tail interval distribution, thereby providing a solid reason as to why it makes sense to consider Lévy noise in the study of neural systems. Lévy noise has also been extensively used to model many other complex systems, including lasers [66], quantum dots [55], cardiac dynamics [60], molecular motor [41], economics [74,2], and social systems [63], where changes are often abrupt [14,87].…”

Section: Introductionmentioning

confidence: 99%

Lévy Noise-induced Self-induced Stochastic Resonance in a Memristive Neuron

Yamakou

Tran

2021

Preprint

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Self-induced stochastic resonance (SISR) is a subtle resonance mechanism requiring a nontrivial scaling limit between the stochastic and the deterministic timescales of an excitable system, leading to the emergence of a limit cycle behavior which is absent without noise. All previous studies on SISR in neural systems have only considered the idealized Gaussian white noise. Moreover, these studies have ignored one electrophysiological aspect of the nerve cell: its memristive properties. In this paper, first, we show that in the excitable regime, the asymptotic matching of the mean escape timescale of an α-stable Lévy process (with value increasing as a power σ-α of the noise amplitude σ, unlike the mean escape timescale of a Gaussian process with the value increasing as in Kramers' law) and the deterministic timescale (controlled by the singular parameter) can also induce a strong SISR. In addition, it is shown that the degree of SISR induced by Lévy noise is not always higher than that of Gaussian noise. Second, we show that, for both types of noises, the two memristive properties of the neuron have opposite effects on the degree of SISR: the stronger the feedback gain parameter that controls the modulation of the membrane potential with the magnetic flux and the weaker the feedback gain parameter that controls the saturation of the magnetic flux, the higher the degree of SISR. Finally, we show that, for both types of noises, the degree of SISR in the memristive neuron is always higher than in the non-memristive neuron. Our results could find applications in designing neuromorphic circuits operating in noisy regimes.

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Stepping molecular motor amid Lévy white noise

Cited by 93 publications

References 66 publications

Boltzmann-distribution-equivalent for Lévy noise and how it leads to thermodynamically consistent epicatalysis

Boltzmann-distribution-equivalent for Lévy noise and how it leads to thermodynamically consistent epicatalysis

Lévy noise-induced self-induced stochastic resonance in a memristive neuron

Lévy Noise-induced Self-induced Stochastic Resonance in a Memristive Neuron

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