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Rhythmic and sequential subdivision of the elongating vertebrate embryonic body axis into morphological somites is controlled by an oscillating multicellular genetic network termed the segmentation clock. This clock operates in the…
Rhythmic and sequential segmentation of the embryonic body plan is a vital developmental patterning process in all vertebrate species. However, a theoretical framework capturing the emergence of dynamic patterns of gene expression from the…
We propose a unified mechanism that reproduces the sequence of dynamical transitions observed during somitogenesis, the process of body segmentation during embryonic development, that is invariant across all vertebrate species. This is…
The clock and wavefront paradigm is arguably the most widely accepted model for explaining the embryonic process of somitogenesis. According to this model, somitogenesis is based upon the interaction between a genetic oscillator, known as…
In most vertebrate species, the body axis is generated by the formation of repeated transient structures called somites. This spatial periodicity in somitogenesis has been related to the temporally sustained oscillations in certain mRNAs…
Unveiling the mechanisms through which the somitogenesis regulatory network exerts spatiotemporal control of the somitic patterning has required a combination of experimental and mathematical modeling strategies. Significant progress has…
Synchronization of mobile oscillators occurs in numerous contexts, including physical, chemical, biological and engineered systems. In vertebrate embryonic development, a segmental body structure is generated by a population of mobile…
Circadian clocks play a pivotal role in orchestrating numerous physiological and developmental events. Waveform shapes of the oscillations of protein abundances can be informative about the underlying biochemical processes of circadian…
The migration of cells is relevant for processes such as morphogenesis, wound healing, and invasion of cancer cells. In order to move, single cells deform cyclically. However, it is not understood how these shape oscillations influence…
Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically-motivated mathematical models for cell differentiation that generically generate oscillations and hence…
Coupled biological oscillators can tick with the same period. How this collective period is established is a key question in understanding biological clocks. We explore this question in the segmentation clock, a population of coupled…
We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed,…
In many adult tissues, stem cells and differentiated cells are not homogeneously distributed : stem cells are arranged in periodic "niches", and differentiated cells are constantly produced and migrate out of these niches. In this article,…
Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole…
The mechanical properties of vertebrate bone are largely determined by a process which involves the complex interplay of three different cell types. This process is called {\it bone remodeling}, and occurs asynchronously at multiple sites…
To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein…
Rhythmogenesis, which is critical for many biological functions, involves a transition to coherent activity through cell-cell communication. In the absence of centralized coordination by specialized cells (pacemakers), competing oscillating…
Biological rhythms are generated by pacemaker organs, such as the heart pacemaker organ (the sinoatrial node) and the master clock of the circadian rhythms (the suprachiasmatic nucleus), which are composed of a network of autonomously…
The timing of cell divisions in early embryos during the In-Vitro Fertilization (IVF) process is a key predictor of embryo viability. However, observing cell divisions in Time-Lapse Monitoring (TLM) is a time-consuming process and highly…
In an oscillatory medium, a region which oscillates faster than its surroundings can act as a source of outgoing waves. Such pacemaker-generated waves can synchronize the whole medium and are present in many chemical and biological systems,…