Internal noise enhanced detection of hormonal signal through intracellular calcium oscillations

Detection of weak signals in memory thermal baths

The nonlinear relaxation time and the statistics of the first passage time distribution in connection with the quasideterministic approach are used to detect weak signals in the decay process of the unstable state of a Brownian particle embedded in memory thermal baths. The study is performed in the overdamped approximation of a generalized Langevin equation characterized by an exponential decay in the friction memory kernel. A detection criterion for each time scale is studied: The first one is referred to as the receiver output, which is given as a function of the nonlinear relaxation time, and the second one is related to the statistics of the first passage time distribution.

Detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field

The detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field is studied in the dynamical relaxation of the unstable state, characterized by a two-dimensional bistable potential. The detection process depends on a dimensionless quantity referred to as the receiver output, calculated as a function of the nonlinear relaxation time and being a characteristic time scale of our system. The latter characterizes the complete dynamical relaxation of the Brownian particle as it relaxes from the initial unstable state of the bistable potential to its corresponding steady state. The one-dimensional problem is also studied to complement the description.

Detection of weak and large electric fields through the transient dynamics of a Brownian particle in an electromagnetic field

In this work we present a mechanism to detect the presence of an external electric field of either weak or large amplitude by means of the decay process from an unstable state, described by a bistable potential, of an electrically charged Brownian particle embedded in a uniform electromagnetic field. Since the detection process takes place around the initial unstable state of the bistable potential, our theoretical description is given in the linear approximation of the aforementioned potential. The decay process is characterized through the statistics of the passage time distribution calculated by means of two theoretical approaches relying on the overdamped Langevin equation: one is the quasideterministic approach valid for large times and used for the detection of weak signals, whereas the other one is the rotational approach, valid for intermediate times and adequate for the detection of large electric-field amplitudes.

Error-probability noise benefits in threshold neural signal detection

Five new theorems and a stochastic learning algorithm show that noise can benefit threshold neural signal detection by reducing the probability of detection error. The first theorem gives a necessary and sufficient condition for such a noise benefit when a threshold neuron performs discrete binary signal detection in the presence of additive scale-family noise. The theorem allows the user to find the optimal noise probability density for several closed-form noise types that include generalized Gaussian noise. The second theorem gives a noise-benefit condition for more general threshold signal detection when the signals have continuous probability densities. The third and fourth theorems reduce this noise benefit to a weighted-derivative comparison of signal probability densities at the detection threshold when the signal densities are continuously differentiable and when the noise is symmetric and comes from a scale family. The fifth theorem shows how collective noise benefits can occur in a parallel array of threshold neurons even when an individual threshold neuron does not itself produce a noise benefit. The stochastic gradient-ascent learning algorithm can find the optimal noise value for noise probability densities that do not have a closed form.

Establishing the stochastic nature of intracellular calcium oscillations from experimental data

Calcium has been established as a key messenger in both intra- and intercellular signaling. Experimentally observed intracellular calcium responses to different agonists show a variety of behaviors from simple spiking to complex oscillatory regimes. Here we study typical experimental traces of calcium oscillations in hepatocytes obtained in response to phenylephrine and ATP. The traces were analyzed with methods of nonlinear time series analysis in order to determine the stochastic/deterministic nature of the intracellular calcium oscillations. Despite the fact that the oscillations appear, visually, to be deterministic yet perturbed by noise, our analyses provide strong evidence that the measured calcium traces in hepatocytes are prevalently of stochastic nature. In particular, bursting calcium oscillations are temporally correlated Gaussian series distorted by a monotonic, instantaneous, time-independent function, whilst the spiking behavior appears to have a dynamical nonlinear component whereby the overall determinism level is still low. The biological importance of this finding is discussed in relation to the mechanisms incorporated in mathematical models as well as the role of stochasticity and determinism at cellular and tissue levels which resemble typical statistical and thermodynamic effects in physics.

Spatial coherence resonance in excitable biochemical media induced by internal noise

We show that in a spatially extended excitable medium, presently modelled with diffusively coupled FitzHugh-Nagumo neurons, internal stochasticity is able to extract a characteristic spatial frequency of waves on the spatial grid. Internal noise is introduced via a stochastic simulation method and is the only agent acting on the system. Remarkably, the spatial periodicity is best pronounced at an intermediate level of internal stochasticity. Thus, the reported phenomenon is an observation of internal noise spatial coherence resonance in excitable biochemical media.

Coupling and internal noise sustain synchronized oscillation in calcium system

In this work, the effects of coupling on two calcium subsystems were investigated, the cooperation between coupling and internal noise was also considered. When two non-identical subsystems are in steady state, coupling can induce oscillations, and distinctly enlarge the oscillatory region in bifurcation diagram. Besides, coupling can make the two non-identical oscillators synchronized. With the increment of the coupling strength, the cross-correlation time of the two oscillators firstly increases and then decreases to be constant, showing the synchronization without tuning coupling strength. When internal noise is considered, similar phenomena can also be obtained under the cooperation between coupling and internal noise.

Structural-diversity-enhanced cellular ability to detect subthreshold extracellular signals

We study the influence of the structural diversity of cells on subthreshold agonist signals in coupled hepatocytes systems. The variance of the cellular structural parameter sigma is employed to characterize the structural diversity. It is found that structural diversity enhances the cellular ability to detect extracellular weak signals through intracellular Ca2+ oscillations and the regularity of Ca2+ spikes undergoes a maximum with a variation of sigma, indicating the occurrence of structural-diversity-induced coherence resonance. Furthermore, the effects of the level of subthreshold stimulus and junctional coupling strength on the behavior of Ca2+ dynamics are also considered. Analysis indicates that these phenomena have inherent relevance to both the bifurcation feature of a single cell and intercellular interaction through junctional coupling. Our findings may exhibit that structural diversity plays a constructive role in biological systems.

A mesoscopic stochastic mechanism of cytosolic calcium oscillations

Based on a model of intracellular calcium (Ca(2+)) oscillation with self-modulation of inositol 1,4,5-trisphosphate signal, the mesoscopic stochastic differential equations for the intracellular Ca(2+) oscillations are theoretically derived by using the chemical Langevin equation method. The effects of the finite biochemical reaction molecule number on both simple and complex cytosolic Ca(2+) oscillations are numerically studied. In the case of simple intracellular Ca(2+) oscillation, it is found that, with the increase of molecule number, the coherence resonance or autonomous resonance phenomena can occur for some external stimulation parameter values. In the cases of complex cytosolic Ca(2+) oscillations, each extremum of concentration of cytosolic Ca(2+) oscillations corresponds to a peak in the histogram of Ca(2+) concentration, and the most probability appeared during the bursting plateau level for bursting, but at the largest minimum of Ca(2+) concentration for chaos. For quasi-periodicity, however, there are only two peaks in the histogram of Ca(2+) concentration, and the most probability is located at low concentration state.

A quantitative kinetic model for ATP-induced intracellular Ca2+ oscillations

A quantitative kinetic model is proposed to simulate the ATP-induced intracellular Ca(2+) oscillations. The quantitative effect of ATP concentration upon the oscillations was successfully simulated. Our simulation results support previous experimental explanations that the Ca(2+) oscillations are mainly due to interaction of Ca(2+) release from the endoplasmic reticulum (ER) and the ATP-dependent Ca(2+) pump back into the ER, and the oscillations are prolonged by extracellular Ca(2+) entry that maintains the constant Ca(2+) supplies to its intracellular stores. The model is also able to simulate the sudden disappearance phenomenon of the Ca(2+) oscillations observed in some cell types by taking into account of the biphasic characteristic of the Ca(2+) release from the endoplasmic reticulum (ER). Moreover, the model simulation results for the Ca(2+) oscillations characteristics such as duration, peak [Ca(2+)](cyt), and average interval, etc., lead to prediction of some possible factors responsible for the variations of Ca(2+) oscillations in different types of cells.

Enhancement of internal-noise coherence resonance by modulation of external noise in a circadian oscillator

A circadian oscillator driven by external noise and internal noise has been studied by use of the chemical Langevin equation method. When the system is near a Hopf bifurcation and driven by internal noise only, it is found that the coherence resonance phenomenon can be induced by the internal noise. When the system is simultaneously driven by internal and external noise, it is found that external-noise coherence resonance can be suppressed by internal noise, while internal-noise coherence resonance can be enhanced by modulation of the external noise intensity in a certain range of noise intensity. Another interesting result is that the external noise can regulate the optimal system size when the internal-noise coherence resonance occurs.