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Notch signaling regulates tissue morphogenesis through cell-cell interactions. The Notch effectors Hes1 and Hes7 are expressed in an oscillatory manner and regulate developmental processes such as neurogenesis and somitogenesis, respectively. Expression of the mRNA for the mouse Notch ligand Delta-like1 (Dll1) is also oscillatory. However, the dynamics of Dll1 protein expression are controversial, and their functional significance is unknown. Here, we developed a live-imaging system and found that Dll1 protein expression oscillated in neural progenitors and presomitic mesoderm cells. Notably, when Dll1 expression was accelerated or delayed by shortening or elongating the Dll1 gene, Dll1 oscillations became severely dampened or quenched at intermediate levels, as modeled mathematically. Under this condition, Hes1 and Hes7 oscillations were also dampened. In the presomitic mesoderm, steady Dll1 expression led to severe fusion of somites and their derivatives, such as vertebrae and ribs. In the developing brain, steady Dll1 expression inhibited proliferation of neural progenitors and accelerated neurogenesis, whereas optogenetic induction of Dll1 oscillation efficiently maintained neural progenitors. These results indicate that the appropriate timing of Dll1 expression is critical for the oscillatory networks and suggest the functional significance of oscillatory cell-cell interactions in tissue morphogenesis., (© 2016 Shimojo et al.; Published by Cold Spring Harbor Laboratory Press.)

Spike-timing dependent plasticity (STDP) is an organizing principle of biological neural networks. While synchronous firing of neurons is considered to be an important functional block in the brain, how STDP shapes neural networks possibly toward synchrony is not entirely clear. We examine relations between STDP and synchronous firing in spontaneously firing neural populations. Using coupled heterogeneous phase oscillators placed on initial networks, we show numerically that STDP prunes some synapses and promotes formation of a feedforward network. Eventually a pacemaker, which is the neuron with the fastest inherent frequency in our numerical simulations, emerges at the root of the feedforward network. In each oscillatory cycle, a packet of neural activity is propagated from the pacemaker to downstream neurons along layers of the feedforward network. This event occurs above a clear-cut threshold value of the initial synaptic weight. Below the threshold, neurons are self-organized into separate clusters each of which is a feedforward network.

Spike-timing-dependent plasticity (STDP) with asymmetric learning windows is commonly found in the brain and useful for a variety of spike-based computations such as input filtering and associative memory. A natural consequence of STDP is establishment of causality in the sense that a neuron learns to fire with a lag after specific presynaptic neurons have fired. The effect of STDP on synchrony is elusive because spike synchrony implies unitary spike events of different neurons rather than a causal delayed relationship between neurons. We explore how synchrony can be facilitated by STDP in oscillator networks with a pacemaker. We show that STDP with asymmetric learning windows leads to self-organization of feedforward networks starting from the pacemaker. As a result, STDP drastically facilitates frequency synchrony. Even though differences in spike times are lessened as a result of synaptic plasticity, the finite time lag remains so that perfect spike synchrony is not realized. In contrast to traditional mechanisms of large-scale synchrony based on mutual interaction of coupled neurons, the route to synchrony discovered here is enslavement of downstream neurons by upstream ones. Facilitation of such feedforward synchrony does not occur for STDP with symmetric learning windows.

Entrainment by a pacemaker, representing an element with a higher frequency, is numerically investigated for several classes of random networks which consist of identical phase oscillators. We find that the entrainment frequency window of a network decreases exponentially with its depth, defined as the mean forward distance of the elements from the pacemaker. Effectively, only shallow networks can thus exhibit frequency locking to the pacemaker. The exponential dependence is also derived analytically as an approximation for large random asymmetric networks.