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Guckenheimer, John; Harris-Warrick, Ronald M.; Peck, Jack H.; Willms, Allan R.

doi:10.1023/a:1008871803040

Cited by 103 publications

(37 citation statements)

References 5 publications

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“…It then turns out that, as a result, we must rescale time to be in the terminal boundary solution. Such an approach has been studied extensively by Guckenheimer in the Morris-Lecar and Hodgkin-Huxley neurons with adaptation, as well as general systems that support canards of this type [55], [56]. Nonetheless, we proceed by carrying out a similar calculation here and use it to derive an approximate formula for the period of the solution.…”

Section: Resultsmentioning

confidence: 99%

Sparse Gamma Rhythms Arising through Clustering in Adapting Neuronal Networks

Kilpatrick

Ermentrout

2011

PLoS Comput Biol

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Gamma rhythms (30–100 Hz) are an extensively studied synchronous brain state responsible for a number of sensory, memory, and motor processes. Experimental evidence suggests that fast-spiking interneurons are responsible for carrying the high frequency components of the rhythm, while regular-spiking pyramidal neurons fire sparsely. We propose that a combination of spike frequency adaptation and global inhibition may be responsible for this behavior. Excitatory neurons form several clusters that fire every few cycles of the fast oscillation. This is first shown in a detailed biophysical network model and then analyzed thoroughly in an idealized model. We exploit the fact that the timescale of adaptation is much slower than that of the other variables. Singular perturbation theory is used to derive an approximate periodic solution for a single spiking unit. This is then used to predict the relationship between the number of clusters arising spontaneously in the network as it relates to the adaptation time constant. We compare this to a complementary analysis that employs a weak coupling assumption to predict the first Fourier mode to destabilize from the incoherent state of an associated phase model as the external noise is reduced. Both approaches predict the same scaling of cluster number with respect to the adaptation time constant, which is corroborated in numerical simulations of the full system. Thus, we develop several testable predictions regarding the formation and characteristics of gamma rhythms with sparsely firing excitatory neurons.

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Section: Resultsmentioning

confidence: 99%

Sparse Gamma Rhythms Arising through Clustering in Adapting Neuronal Networks

Kilpatrick

Ermentrout

2011

PLoS Comput Biol

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“…This threshold activation is achieved through a transcritical bifurcation (Fig. 3a) (Guckenheimer et al, 1997). At any E2F values, two steady states for Cyclin B exist, one zero and one either negative (below the threshold) or positive (above the threshold).…”

Section: A Switch In Cyclin B Activity Drives M Phase Progressionmentioning

confidence: 99%

“…When the degradation rate is reduced, a second stable steady state appears through a saddle-node bifurcation. These two stable steady states co-exist until the low level steady state becomes unstable, through a reverse pitchfork bifurcation (Guckenheimer et al, 1997). For degradation rates below that level, there is only high Cyclin B activity.…”

Section: A Switch In Cyclin B Activity Drives M Phase Progressionmentioning

confidence: 99%

Regulation of mammalian cell cycle progression in the regenerating liver

Chauhan

Lorenzen

Herzel

et al. 2011

Journal of Theoretical Biology

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The process of cell division in mammalian cells is orchestrated by cell-cycle-dependent oscillations of cyclin protein levels. Cyclin levels are controlled by redundant transcriptional, post-translational and degradation feedback loops. How each of these separate loops contributes to the regulation of the key cell cycle events and to the connection between the G1-S transition and the subsequent mitotic events is under investigation. Here, we present an integrated computational model of the mammalian cell cycle based on the sequential activation of cyclins. We validate the model against experimental data on liver cells (hepatocytes), which undergo one or two rounds of synchronous circadian-clock gated cell divisions during liver regeneration, after partial hepatectomy (PH). The model exhibits bandpass filter properties that allow the system to ignore strong but transient, or sustained but weak damages after PH. Bifurcation analysis of the model suggests two different threshold mechanisms for the progression of the cell through mitosis. These results are coherent with the notion that the mitotic exit in mammalian cells is bistable, and suggests that Cdc20 homologue 1 (Cdh1) is an important regulator of mitosis. Regulation by Cdh1 also explains the observed G2/M phase prolongation after hepatocyte growth factor (HGF) stimulation during S phase.

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“…5(b)) of this type 2 is different from that of the normal type 2. Note that the drug-induced type 2 cell fires with a fast adaptation phenomenon (Guckenheimer et al 1997) (Fig. 4(c)).…”

Section: Resultsmentioning

confidence: 97%

Transition between two excitabilities in mesencephalic V neurons

Liu

Yang

2007

J Comput Neurosci

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Neurons can make different responses to identical inputs. According to the emerging frequency of repetitive firing, neurons are classified into two types: type 1 and type 2 excitability. Though in mathematical simulations, minor modifications of parameters describing ionic currents can result in transitions between these two excitabilities, empirical evidence to support these theoretical possibilities is scarce. Here we report a joint theoretical and experimental study to test the hypothesis that changes in parameters describing ionic currents cause predictable transitions between the two excitabilities in mesencephalic V (Mes V) neurons. We developed a simple mathematical model of Mes V neurons. Using bifurcation analysis and model simulation, we then predicted that changes in conductance of two low-threshold currents would result in transitions between type 1 and type 2. Finally, by applying specific channel blockers, we observed the transition between two excitabilities forecast by the mathematical model.

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Untitled

Cited by 103 publications

References 5 publications

Sparse Gamma Rhythms Arising through Clustering in Adapting Neuronal Networks

Sparse Gamma Rhythms Arising through Clustering in Adapting Neuronal Networks

Regulation of mammalian cell cycle progression in the regenerating liver

Transition between two excitabilities in mesencephalic V neurons

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