409 research outputs found
Transient Resetting: A Novel Mechanism for Synchrony and Its Biological Examples
The study of synchronization in biological systems is essential for the
understanding of the rhythmic phenomena of living organisms at both molecular
and cellular levels. In this paper, by using simple dynamical systems theory,
we present a novel mechanism, named transient resetting, for the
synchronization of uncoupled biological oscillators with stimuli. This
mechanism not only can unify and extend many existing results on (deterministic
and stochastic) stimulus-induced synchrony, but also may actually play an
important role in biological rhythms. We argue that transient resetting is a
possible mechanism for the synchronization in many biological organisms, which
might also be further used in medical therapy of rhythmic disorders. Examples
on the synchronization of neural and circadian oscillators are presented to
verify our hypothesis.Comment: 17 pages, 7 figure
Corticothalamic projections control synchronization in locally coupled bistable thalamic oscillators
Thalamic circuits are able to generate state-dependent oscillations of
different frequencies and degrees of synchronization. However, only little is
known how synchronous oscillations, like spindle oscillations in the thalamus,
are organized in the intact brain. Experimental findings suggest that the
simultaneous occurrence of spindle oscillations over widespread territories of
the thalamus is due to the corticothalamic projections, as the synchrony is
lost in the decorticated thalamus. Here we study the influence of
corticothalamic projections on the synchrony in a thalamic network, and uncover
the underlying control mechanism, leading to a control method which is
applicable in wide range of stochastic driven excitable units.Comment: 4 pages with 4 figures (Color online on p.3-4) include
Short Conduction Delays Cause Inhibition Rather than Excitation to Favor Synchrony in Hybrid Neuronal Networks of the Entorhinal Cortex
How stable synchrony in neuronal networks is sustained in the presence of conduction delays is an open question. The Dynamic Clamp was used to measure phase resetting curves (PRCs) for entorhinal cortical cells, and then to construct networks of two such neurons. PRCs were in general Type I (all advances or all delays) or weakly type II with a small region at early phases with the opposite type of resetting. We used previously developed theoretical methods based on PRCs under the assumption of pulsatile coupling to predict the delays that synchronize these hybrid circuits. For excitatory coupling, synchrony was predicted and observed only with no delay and for delays greater than half a network period that cause each neuron to receive an input late in its firing cycle and almost immediately fire an action potential. Synchronization for these long delays was surprisingly tight and robust to the noise and heterogeneity inherent in a biological system. In contrast to excitatory coupling, inhibitory coupling led to antiphase for no delay, very short delays and delays close to a network period, but to near-synchrony for a wide range of relatively short delays. PRC-based methods show that conduction delays can stabilize synchrony in several ways, including neutralizing a discontinuity introduced by strong inhibition, favoring synchrony in the case of noisy bistability, and avoiding an initial destabilizing region of a weakly type II PRC. PRCs can identify optimal conduction delays favoring synchronization at a given frequency, and also predict robustness to noise and heterogeneity
Phase resetting reveals network dynamics underlying a bacterial cell cycle
Genomic and proteomic methods yield networks of biological regulatory
interactions but do not provide direct insight into how those interactions are
organized into functional modules, or how information flows from one module to
another. In this work we introduce an approach that provides this complementary
information and apply it to the bacterium Caulobacter crescentus, a paradigm
for cell-cycle control. Operationally, we use an inducible promoter to express
the essential transcriptional regulatory gene ctrA in a periodic, pulsed
fashion. This chemical perturbation causes the population of cells to divide
synchronously, and we use the resulting advance or delay of the division times
of single cells to construct a phase resetting curve. We find that delay is
strongly favored over advance. This finding is surprising since it does not
follow from the temporal expression profile of CtrA and, in turn, simulations
of existing network models. We propose a phenomenological model that suggests
that the cell-cycle network comprises two distinct functional modules that
oscillate autonomously and couple in a highly asymmetric fashion. These
features collectively provide a new mechanism for tight temporal control of the
cell cycle in C. crescentus. We discuss how the procedure can serve as the
basis for a general approach for probing network dynamics, which we term
chemical perturbation spectroscopy (CPS)
Detecting Directed Interactions of Networks by Random Variable Resetting
We propose a novel method of detecting directed interactions of a general
dynamic network from measured data. By repeating random state variable
resetting of a target node and appropriately averaging over the measurable
data, the pairwise coupling function between the target and the response nodes
can be inferred. This method is applicable to a wide class of networks with
nonlinear dynamics, hidden variables and strong noise. The numerical results
have fully verified the validity of the theoretical derivation
Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise
We extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. The master equation formulation of stochastic neurodynamics represents the state of each population by the number of currently active neurons, and the state transitions are chosen so that deterministic Wilson-Cowan rate equations are recovered in the mean-field limit. We apply phase reduction and averaging methods to a corresponding Langevin approximation of the master equation in order to determine how intrinsic noise disrupts synchronization of the population oscillators driven by a common extrinsic noise source. We illustrate our analysis by considering one of the simplest networks known to generate limit cycle oscillations at the population level, namely, a pair of mutually coupled excitatory (E) and inhibitory (I) subpopulations. We show how the combination of intrinsic independent noise and extrinsic common noise can lead to clustering of the population oscillators due to the multiplicative nature of both noise sources under the Langevin approximation. Finally, we show how a similar analysis can be carried out for another simple population model that exhibits limit cycle oscillations in the deterministic limit, namely, a recurrent excitatory network with synaptic depression; inclusion of synaptic depression into the neural master equation now generates a stochastic hybrid system
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