Amplitude Death Induced by Intrinsic Noise in a System of Three Coupled Stochastic Brusselators

In this work, we study the interplay between intrinsic biochemical noise and the diffusive coupling, in an array of three stochastic Brusselators that present a limit-cycle dynamics. The stochastic dynamics is simulated by means of the Gillespie algorithm. The intensity of the intrinsic biochemical noise is regulated by changing the value of the system volume (Ω), while keeping constant the chemical species' concentration. To characterize the system behavior, we measure the average spike amplitude (ASA), the order parameter R, the average interspike interval (ISI), and the coefficient of variation (CV) for the interspike interval. By analyzing how these measures depend on Ω and the coupling strength, we observe that when the coupling parameter is different from zero, increasing the level of intrinsic noise beyond a given threshold suddenly drives the spike amplitude, SA, to zero and makes ISI increase exponentially. These results provide numerical evidence that amplitude death (AD) takes place via a homoclinic bifurcation.

Download Full-text

Noise control for molecular computing

Journal of The Royal Society Interface ◽

10.1098/rsif.2018.0199 ◽

2018 ◽

Vol 15 (144) ◽

pp. 20180199 ◽

Cited By ~ 3

Author(s):

Tomislav Plesa ◽

Konstantinos C. Zygalakis ◽

David F. Anderson ◽

Radek Erban

Keyword(s):

Stochastic Dynamics ◽

Noise Control ◽

Reaction System ◽

Reaction Network ◽

Intrinsic Noise ◽

Biochemical Networks ◽

Mass Action ◽

Mass Action Kinetics ◽

Interdisciplinary Field ◽

Biochemical Systems

Synthetic biology is a growing interdisciplinary field, with far-reaching applications, which aims to design biochemical systems that behave in a desired manner. With the advancement in nucleic-acid-based technology in general, and strand-displacement DNA computing in particular, a large class of abstract biochemical networks may be physically realized using nucleic acids. Methods for systematic design of the abstract systems with prescribed behaviours have been predominantly developed at the (less-detailed) deterministic level. However, stochastic effects, neglected at the deterministic level, are increasingly found to play an important role in biochemistry. In such circumstances, methods for controlling the intrinsic noise in the system are necessary for a successful network design at the (more-detailed) stochastic level. To bridge the gap, the noise-control algorithm for designing biochemical networks is developed in this paper. The algorithm structurally modifies any given reaction network under mass-action kinetics, in such a way that (i) controllable state-dependent noise is introduced into the stochastic dynamics, while (ii) the deterministic dynamics are preserved. The capabilities of the algorithm are demonstrated on a production–decay reaction system, and on an exotic system displaying bistability. For the production–decay system, it is shown that the algorithm may be used to redesign the network to achieve noise-induced multistability. For the exotic system, the algorithm is used to redesign the network to control the stochastic switching, and achieve noise-induced oscillations.

Download Full-text

The chemical Langevin equation for biochemical systems in dynamic environments

10.1101/2021.12.19.473404 ◽

2021 ◽

Author(s):

Lucy Ham ◽

Megan Coomer ◽

Michael P.H. Stumpf

Keyword(s):

Langevin Equation ◽

Stochastic Dynamics ◽

Computational Simulation ◽

Intrinsic Noise ◽

Simulation Method ◽

Reaction Networks ◽

Biochemical Reaction Networks ◽

Extrinsic Noise ◽

Chemical Langevin Equation ◽

Biochemical Systems

Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly stem from the interplay of the network with many other - and mostly unknown - fluctuating processes, as well as with various random signals arising from the extracellular world; these sources contribute extrinsic noise. Here we provide a computational simulation method to probe the stochastic dynamics of biochemical systems subject to both intrinsic and extrinsic noise. We develop an extrinsic chemical Langevin equation - a physically motivated extension of the chemical Langevin equation - to model intrinsically noisy reaction networks embedded in a stochastically fluctuating environment. The extrinsic CLE is a continuous approximation to the Chemical Master Equation (CME) with time-varying propensities. In our approach, noise is incorporated at the level of the CME, and can account for the full dynamics of the exogenous noise process, irrespective of timescales and their mismatches. We show that our method accurately captures the first two moments of the stationary probability density when compared with exact stochastic simulation methods, while reducing the computational runtime by several orders of magnitude. Our approach provides a method that is practical, computationally efficient and physically accurate to study systems that are simultaneously subject to a variety of noise sources.

Download Full-text

Enhanced signal-to-noise ratios in frog hearing can be achieved through amplitude death

Journal of The Royal Society Interface ◽

10.1098/rsif.2013.0525 ◽

2013 ◽

Vol 10 (87) ◽

pp. 20130525 ◽

Cited By ~ 8

Author(s):

Kang-Hun Ahn

Keyword(s):

High Sensitivity ◽

Intrinsic Noise ◽

Low Noise ◽

Great Sensitivity ◽

High Signal ◽

Mechanical Stimuli ◽

Signal To Noise ◽

Amplitude Death ◽

Hair Bundles

In the ear, hair cells transform mechanical stimuli into neuronal signals with great sensitivity, relying on certain active processes. Individual hair cell bundles of non-mammals such as frogs and turtles are known to show spontaneous oscillation. However, hair bundles in vivo must be quiet in the absence of stimuli, otherwise the signal is drowned in intrinsic noise. Thus, a certain mechanism is required in order to suppress intrinsic noise. Here, through a model study of elastically coupled hair bundles of bullfrog sacculi, we show that a low stimulus threshold and a high signal-to-noise ratio (SNR) can be achieved through the amplitude death phenomenon (the cessation of spontaneous oscillations by coupling). This phenomenon occurs only when the coupled hair bundles have inhomogeneous distribution, which is likely to be the case in biological systems. We show that the SNR has non-monotonic dependence on the mass of the overlying membrane, and find out that the SNR has maximum value in the region of amplitude death. The low threshold of stimulus through amplitude death may account for the experimentally observed high sensitivity of frog sacculi in detecting vibration. The hair bundles' amplitude death mechanism provides a smart engineering design for low-noise amplification.

Download Full-text

Identification and Continuity of the Distributions of Burst-Length and Interspike Intervals in the Stochastic Morris-Lecar Neuron

Neural Computation ◽

10.1162/neco_a_00209 ◽

2011 ◽

Vol 23 (12) ◽

pp. 3094-3124 ◽

Cited By ~ 12

Author(s):

Peter F. Rowat ◽

Priscilla E. Greenwood

Keyword(s):

Interspike Interval ◽

Stochastic Dynamics ◽

Model Neuron ◽

Quantitative Description ◽

Current Drive ◽

Channel Noise ◽

Sequence Length ◽

Applied Current ◽

Interspike Interval Distribution ◽

Interval Distribution

Using the Morris-Lecar model neuron with a type II parameter set and K+-channel noise, we investigate the interspike interval distribution as increasing levels of applied current drive the model through a subcritical Hopf bifurcation. Our goal is to provide a quantitative description of the distributions associated with spiking as a function of applied current. The model generates bursty spiking behavior with sequences of random numbers of spikes (bursts) separated by interburst intervals of random length. This kind of spiking behavior is found in many places in the nervous system, most notably, perhaps, in stuttering inhibitory interneurons in cortex. Here we show several practical and inviting aspects of this model, combining analysis of the stochastic dynamics of the model with estimation based on simulations. We show that the parameter of the exponential tail of the interspike interval distribution is in fact continuous over the entire range of plausible applied current, regardless of the bifurcations in the phase portrait of the model. Further, we show that the spike sequence length, apparently studied for the first time here, has a geometric distribution whose associated parameter is continuous as a function of applied current over the entire input range. Hence, this model is applicable over a much wider range of applied current than has been thought.

Download Full-text

Chemical Species Identification in an SEM by Changes in Emitted X-Ray Energies

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100052869 ◽

1974 ◽

Vol 32 ◽

pp. 570-571

Author(s):

R. H. Duff

Keyword(s):

Species Identification ◽

Valence Electron ◽

Chemical Species ◽

X Rays ◽

Chemical Bonds ◽

Small Shift ◽

X Ray ◽

Electron Transitions ◽

Peak Energy ◽

Chemical Combination

A material irradiated with electrons emits x-rays having energies characteristic of the elements present. Chemical combination between elements results in a small shift of the peak energies of these characteristic x-rays because chemical bonds between different elements have different energies. The energy differences of the characteristic x-rays resulting from valence electron transitions can be used to identify the chemical species present and to obtain information about the chemical bond itself. Although these peak-energy shifts have been well known for a number of years, their use for chemical-species identification in small volumes of material was not realized until the development of the electron microprobe.

Download Full-text

Confocal Raman mapping

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100132200 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1514-1515

Author(s):

J. Barbillat ◽

M. Delhaye ◽

P. Dhamelincourt

Keyword(s):

Chemical Species ◽

Diffraction Limit ◽

Microscopic Level ◽

Raman Mapping ◽

Complete Spectrum ◽

Laser Illumination ◽

Ccd Detector ◽

Raman Microprobe ◽

Photodiode Array ◽

Raman Image

Raman mapping, with a spatial resolution close to the diffraction limit, can help to reveal the distribution of chemical species at the surface of an heterogeneous sample.As early as 1975,three methods of sample laser illumination and detector configuration have been proposed to perform Raman mapping at the microscopic level (Fig. 1),:- Point illumination:The basic design of the instrument is a classical Raman microprobe equipped with a PM tube or either a linear photodiode array or a two-dimensional CCD detector. A laser beam is focused on a very small area ,close to the diffraction limit.In order to explore the whole surface of the sample,the specimen is moved sequentially beneath the microscope by means of a motorized XY stage. For each point analyzed, a complete spectrum is obtained from which spectral information of interest is extracted for Raman image reconstruction.- Line illuminationA narrow laser line is focused onto the sample either by a cylindrical lens or by a scanning device and is optically conjugated with the entrance slit of the stigmatic spectrograph.

Download Full-text