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Register a new userFold-Hopf Bursting in a Model for Calcium Signal Transduction
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We study a recent model for calcium signal transduction. This model displays spiking, bursting and chaotic oscillations in accordance with experimental results. We calculate bifurcation diagrams and study the bursting behaviour in detail. This behaviour is classified according to the dynamics of separated slow and fast subsystems. It is shown to be of the Fold-Hopf type, a type which was previously only described in the context of neuronal systems, but not in the context of signal transduction in the cell.
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Signal transduction is an important and basic mechanism to cell life activities. The stochastic state transition of receptor induces the release of singling molecular, which triggers the state transition of other receptors. It constructs a nonlinear singling network, and leads to robust switchlike properties which are critical to biological function. Network architectures and state transitions of receptor will affect the performance of this biological network. In this work, we perform a study of nonlinear signaling on biological network with multistate by analyzing network dynamics of the Ca$^{2+}$ induced Ca$^{2+}$ release mechanism, where fast and slow processes are involved and the receptor has four conformational states. Three types of networks, Erdos-Renyi network, Watts-Strogatz network and BaraBasi-Albert network, are considered with different parameters. The dynamics of the biological networks exhibit different patterns at different time scales. At short time scale, the second open state is essential to reproduce the quasi-bistable regime, which emerges at a critical strength of connection for all three states involved in the fast processes and disappears at another critical point. The pattern at short time scale is not sensitive to the network architecture. At long time scale, only monostable regime is observed, and difference of network architectures affects the results more seriously. Our finding identifies features of nonlinear signaling networks with multistate that may underlie their biological function.
Cells may control fluctuations in protein levels by means of negative autoregulation, where transcription factors bind DNA sites to repress their own production. Theoretical studies have assumed a single binding site for the repressor, while in most species it is found that multiple binding sites are arranged in clusters. We study a stochastic description of negative autoregulation with multiple binding sites for the repressor. We find that increasing the number of binding sites induces regular bursting of gene products. By tuning the threshold for repression, we show that multiple binding sites can also suppress fluctuations. Our results highlight possible roles for the presence of multiple binding sites of negative autoregulators.
This study presents a comprehensive analytic description in terms of the empirical whole minus sum version of Integrated Information in comparison to the decoder based version for the spiking-bursting discrete-time, discrete-state stochastic model, which was recently introduced to describe a specific type of dynamics in a neuron-astrocyte network. The whole minus sum information may change sign, and an interpretation of this transition in terms of net synergy is available in the literature. This motivates our particular interest to the sign of the whole minus sum information in our analytical consideration. The behavior of the whole minus sum and decoder based information measures are found to bear a lot of similarity, showing their mutual asymptotic convergence as time-uncorrelated activity is increased, with the sign transition of the whole minus sum information associated to a rapid growth in the decoder based information. The study aims at creating a theoretical base for using the spiking-bursting model as a well understood reference point for applying Integrated Information concepts to systems exhibiting similar bursting behavior (in particular, to neuron-astrocyte networks). The model can also be of interest as a new discrete-state test bench for different formulations of Integrated Information.
Many cells use calcium signalling to carry information from the extracellular side of the plasma membrane to targets in their interior. Since virtually all cells employ a network of biochemical reactions for Ca2+ signalling, much effort has been devoted to understand the functional role of Ca2+ responses and to decipher how their complex dynamics is regulated by the biochemical network of Ca2+-related signal transduction pathways. Experimental observations show that Ca2+ signals in response to external stimuli encode information via frequency modulation or alternatively via amplitude modulation. Although minimal models can capture separately both types of dynamics, they fail to exhibit different and more advanced encoding modes. By arguments of bifurcation theory, we propose instead that under some biophysical conditions more complex modes of information encoding can also be manifested by minimal models. We consider the minimal model of Li and Rinzel and show that information encoding can occur by amplitude modulation (AM) of Ca2+ oscillations, by frequency modulation (FM) or by both modes (AFM). Our work is motivated by calcium signalling in astrocytes, the predominant type of cortical glial cells that is nowadays recognized to play a crucial role in the regulation of neuronal activity and information processing of the brain. We explain that our results can be crucial for a better understanding of synaptic information transfer. Furthermore, our results might also be important for better insight on other examples of physiological processes regulated by Ca2+ signalling.
Protein phosphorylation cycles are important mechanisms of the post translational modification of a protein and as such an integral part of intracellular signaling and control. We consider the sequential phosphorylation and dephosphorylation of a protein at two binding sites. While it is known that proteins where phosphorylation is processive and dephosphorylation is distributive admit oscillations (for some value of the rate constants and total concentrations) it is not known whether or not this is the case if both phosphorylation and dephosphorylation are distributive. We study four simplified mass action models of sequential and distributive phosphorylation and show that for each of those there do not exist rate constants and total concentrations where a Hopf bifurcation occurs. To arrive at this result we use convex parameters to parameterize the steady state and Hurwitz matrices.
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