Theory allows studying why Evolution might select core genetic commitment circuit topologies over alternatives. The nonlinear dynamics of the underlying gene regulation together with the unescapable subtle interplay of intrinsic biochemical noise impact the range of possible evolutionary choices. The question of why certain genetic regulation circuits might present robustness to phenotype-delivery breaking over others, is therefore of high interest. Here, the behavior of systematically more complex commitment circuits is studied, in the presence of intrinsic noise, with a focus on two aspects relevant to biology: parameter asymmetry and time-scale separation. We show that phenotype delivery is broken in simple two-and three-gene circuits. In the two-gene circuit, we show how stochastic potential wells of different depths break commitment. In the three-gene circuit, we show that the onset of oscillations breaks the commitment phenotype in a systematic way. Finally, we also show that higher dimensional circuits (four-gene and five-gene circuits) may be intrinsically more robust.

It is believed that thalamic reticular nucleus (TRN) controls spindles and spike-wave discharges (SWD) in seizure or sleeping processes. The dynamical mechanisms of spatiotemporal evolutions between these two types of activity, however, are not well understood. In light of this, we first use a single-compartment thalamocortical neural field model to investigate the effects of TRN on occurrence of SWD and its transition. Results show that the increasing inhibition from TRN to specific relay nuclei (SRN) can lead to the transition of system from SWD to slow-wave oscillation. Specially, it is shown that stimulations applied in the cortical neuronal populations can also initiate the SWD and slow-wave oscillation from the resting states under the typical inhibitory intensity from TRN to SRN. Then, we expand into a 3-compartment coupled thalamocortical model network in linear and circular structures, respectively, to explore the spatiotemporal evolutions of wave states in different compartments. The main results are: (i) for the open-ended model network, SWD induced by stimulus in the first compartment can be transformed into sleep-like slow UP-DOWN and spindle states as it propagates into the downstream compartments; (ii) for the close-ended model network, weak stimulations performed in the first compartment can result in the consistent experimentally observed spindle oscillations in all three compartments; in contrast, stronger periodic single-pulse stimulations applied in the first compartment can induce periodic transitions between SWD and spindle oscillations. Detailed investigations reveal that multi-attractor coexistence mechanism composed of SWD, spindles and background state underlies these state evolutions. What's more, in order to demonstrate the state evolution stability with respect to the topological structures of neural network, we further expand the 3-compartment coupled network into 10-compartment coupled one, with linear and circular structures, and nearest-neighbor (NN) coupled network as well as its realization of small-world (SW) topology via random rewiring, respectively. Interestingly, for the cases of linear and circular connetivities, qualitatively similar results were obtained in addition to the more irregularity of firings. However, SWD can be eventually transformed into the consistent low-amplitude oscillations for both NN and SW networks. In particular, SWD evolves into the slow spindling oscillations and background tonic oscillations within the NN and SW network, respectively. Our modeling and simulation studies highlight the effect of network topology in the evolutions of SWD and spindling oscillations, which provides new insights into the mechanisms of cortical seizures development.

Using the tool of Turing instability for partial differential equations, we investigate the spatiotemporal distributions for solutions of a predatorprey-type reaction-diffusion model with spatiotemporal delay. The linear stability conditions of Turing instability, which induce bifurcation patterns in this model, are obtained. Moreover, according to these conditions, we numerically calculate the bifurcation diagrams by using time delay and the predator rate as parameters. The effects of two parameters in the different bifurcation diagrams are also demonstrated through numerical computations and lead to some spatiotemporal patterns of this model, which enrich the pattern formation of predator-prey models.

No abstract

A variety of firing rhythms can be generated spontaneously in the pre-Bötzinger complex. External stimuli can cause changes in the pattern of the firing rhythm, which may cause different physiological effects in the body. In this study, by the fast and slow time scale dynamics, with one- and two-parameter bifurcation analysis, we study the bursting patterns and their transition mechanisms of the pre-Bötzinger complex under washout filter controller. The results may help us understand the relationship between different firing patterns of neurons and external stimuli, and further reveal the mechanisms of disease due to external stimuli.