Optimal cellular mobility for synchronization arising from the gradual recovery of intercellular interactions

Cell movement and intercellular signaling occur simultaneously during the development of tissues, but little is known about how movement affects signaling. Previous theoretical studies have shown that faster moving cells favor synchronization across a population of locally coupled genetic oscillators. An important assumption in these studies is that cells can immediately interact with their new neighbors after arriving at a new location. However, intercellular interactions in cellular systems may need some time to become fully established. How movement affects synchronization in this situation has not been examined. Here we develop a coupled phase oscillator model in which we consider cell movement and the gradual recovery of intercellular coupling experienced by a cell after movement, characterized by a moving rate and a coupling recovery rate respectively. We find (1) an optimal moving rate for synchronization, and (2) a critical moving rate above which achieving synchronization is not possible. These results indicate that the extent to which movement enhances synchrony is limited by a gradual recovery of coupling. These findings suggest that the ratio of time scales of movement and signaling recovery is critical for information transfer between moving cells.Comment: 18 single column pages + 1 table + 5 figures + Supporting Informatio

Sequential pattern formation governed by signaling gradients

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 interplay of cell oscillations with tissue elongation and shortening and with signaling gradients, is still missing. Here we show that a set of coupled genetic oscillators in an elongating tissue that is regulated by diffusing and advected signaling molecules can account for segmentation as a self-organized patterning process. This system can form a finite number of segments and the dynamics of segmentation and the total number of segments formed depend strongly on kinetic parameters describing tissue elongation and signaling molecules. The model accounts for existing experimental perturbations to signaling gradients, and makes testable predictions about novel perturbations. The variety of different patterns formed in our model can account for the variability of segmentation between different animal species.Comment: 12 pages, 5 figure

A framework for quantification and physical modeling of cell mixing applied to oscillator synchronization in vertebrate somitogenesis

In development and disease, cells move as they exchange signals. One example is found in vertebrate development, during which the timing of segment formation is set by a ‘segmentation clock’, in which oscillating gene expression is synchronized across a population of cells by Delta-Notch signaling. Delta-Notch signaling requires local cell-cell contact, but in the zebrafish embryonic tailbud, oscillating cells move rapidly, exchanging neighbors. Previous theoretical studies proposed that this relative movement or cell mixing might alter signaling and thereby enhance synchronization. However, it remains unclear whether the mixing timescale in the tissue is in the right range for this effect, because a framework to reliably measure the mixing timescale and compare it with signaling timescale is lacking. Here, we develop such a framework using a quantitative description of cell mixing without the need for an external reference frame and constructing a physical model of cell movement based on the data. Numerical simulations show that mixing with experimentally observed statistics enhances synchronization of coupled phase oscillators, suggesting that mixing in the tailbud is fast enough to affect the coherence of rhythmic gene expression. Our approach will find general application in analyzing the relative movements of communicating cells during development and disease.Fil: Uriu, Koichiro. Kanazawa University; JapónFil: Bhavna, Rajasekaran. Max Planck Institute of Molecular Cell Biology and Genetics; Alemania. Max Planck Institute for the Physics of Complex Systems; AlemaniaFil: Oates, Andrew C.. Francis Crick Institute; Reino Unido. University College London; Reino UnidoFil: Morelli, Luis Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigación en Biomedicina de Buenos Aires - Instituto Partner de la Sociedad Max Planck; Argentina. Max Planck Institute for Molecular Physiology; Alemania. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentin

Control of endogenous gene expression timing by introns

Comparison of gene expression from transgenes and endogenous genes with or without introns reveals a time-regulating role of introns in natural biological systems

Nonlinearity arising from noncooperative transcription factor binding enhances negative feedback and promotes genetic oscillations

We study the effects of multiple binding sites in the promoter of a genetic oscillator. We evaluate the regulatory function of a promoter with multiple binding sites in the absence of cooperative binding, and consider different hypotheses for how the number of bound repressors affects transcription rate. Effective Hill exponents of the resulting regulatory functions reveal an increase in the nonlinearity of the feedback with the number of binding sites. We identify optimal configurations that maximize the nonlinearity of the feedback. We use a generic model of a biochemical oscillator to show that this increased nonlinearity is reflected in enhanced oscillations, with larger amplitudes over wider oscillatory ranges. Although the study is motivated by genetic oscillations in the zebrafish segmentation clock, our findings may reveal a general principle for gene regulation.Comment: 11 pages, 8 figure

Synchronization in the presence of distributed delays

We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean of the delay distribution. However, synchronization dynamics is sensitive to the shape of the distribution. In the presence of coupling delays, the synchronization rate can be maximal for a specific value of the coupling strength.Comment: 6 pages, 3 figure

Delayed coupling theory of vertebrate segmentation

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 presomitic mesoderm (PSM), generating dynamic stripe patterns of oscillatory gene-expression across the field of PSM cells. How these spatial patterns, the clock's collective period, and the underlying cellular-level interactions are related is not understood. A theory encompassing temporal and spatial domains of local and collective aspects of the system is essential to tackle these questions. Our delayed coupling theory achieves this by representing the PSM as an array of phase oscillators, combining four key elements: a frequency profile of oscillators slowing across the PSM; coupling between neighboring oscillators; delay in coupling; and a moving boundary describing embryonic axis elongation. This theory predicts that the segmentation clock's collective period depends on delayed coupling. We derive an expression for pattern wavelength across the PSM and show how this can be used to fit dynamic wildtype gene-expression patterns, revealing the quantitative values of parameters controlling spatial and temporal organization of the oscillators in the system. Our theory can be used to analyze experimental perturbations, thereby identifying roles of genes involved in segmentation.Comment: published online 10 December 2008, Adv. Online Pub. HFSP Journal (free access

Synchrony Dynamics During Initiation, Failure, and Rescue of the Segmentation Clock

The “segmentation clock” is thought to coordinate sequential segmentation of the body axis in vertebrate embryos. This clock comprises a multicellular genetic network of synchronized oscillators, coupled by intercellular Delta-Notch signaling. How this synchrony is established and how its loss determines the position of segmentation defects in Delta and Notch mutants are unknown. We analyzed the clock's synchrony dynamics by varying strength and timing of Notch coupling in zebra-fish embryos with techniques for quantitative perturbation of gene function. We developed a physical theory based on coupled phase oscillators explaining the observed onset and rescue of segmentation defects, the clock's robustness against developmental noise, and a critical point beyond which synchrony decays. We conclude that synchrony among these genetic oscillators can be established by simultaneous initiation and self-organization and that the segmentation defect position is determined by the difference between coupling strength and noise

Too Much Interference: Injection of Double-Stranded RNA Has Nonspecific Effects in the Zebrafish Embryo

AbstractWe have investigated the ability of double-stranded RNA (dsRNA) to inhibit gene expression in a vertebrate, the zebrafish, Danio rerio. Injection of dsRNA corresponding to the T-box gene tbx16/spadetail (spt) into early wild-type embryos caused a rapid and dramatic loss of tbx16/spt mRNA in the blastula. mRNAs from the papc, tbx6, and gata1 genes, which depend on tbx16/spt function for their expression, were reduced, apparently mimicking the spt mutant phenotype. However, mRNAs from a number of genes that are unaffected by the spt mutation, such as β catenin, stat3, and no tail, were also lost, indicating that the “interference” effect of tbx16/spt dsRNA was not restricted to the endogenous tbx16/spt mRNA. We compared the effects of injecting dsRNA from the zebrafish tbx16/spadetail, nieuwkoid/bozozok, and Brachyury/no tail genes with dsRNA from the bacterial lacZ gene. In each case the embryos displayed a variable syndrome of abnormalities at 12 and 24 h postfertilization. In blind studies, we could not distinguish between the effects of the various dsRNAs. Consistent with a common effect of dsRNA, regardless of sequence, injection of dsRNA from the lacZ gene was likewise effective in strongly reducing tbx16/spt and β catenin mRNA in the blastula. These findings indicate that, despite published reports, the current methodology of double-stranded RNA interference is not a practical technique for investigating zygotic gene function during early zebrafish development

Reaction wavefront theory of notochord segment patterning

The vertebrate axis is segmented into repetitive structures, the vertebrae. In fish, these segmented structures are thought to form from the paraxial mesoderm and the adjacent notochord. Recent work revealed an autonomous patterning mechanism in the zebrafish notochord, with inputs from the segmented paraxial mesoderm. The notochord pattern is established in a sequential manner, progressing from anterior to posterior. Building on this previous work, here, we propose a reaction wavefront theory describing notochord patterning in zebrafish. The pattern is generated by an activator–inhibitor reaction–diffusion mechanism. Cues from the paraxial mesoderm are introduced as a profile of inhibitor sinks. Reactions are turned on by a wavefront that advances from anterior to posterior. We show that this reaction wavefront ensures that a pattern is formed sequentially, in register with the cues, despite the presence of fluctuations. We find that the velocity and shape of the reaction wavefront can modulate the prevalence of defective patterns. Normal patterning is supported in a wide range of sink profile wavelengths, while a minimum sink strength is required for the pattern to follow the cues. The theory predicts that distinct defect types occur for small or large wavelengths. Thus, the reaction wavefront theory provides a possible scenario for notochord patterning, with testable predictions that prompt future experiments.Fil: Fernández Arancibia, Sol Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigación en Biomedicina de Buenos Aires - Instituto Partner de la Sociedad Max Planck; ArgentinaFil: Oates, Andrew C.. Ecole Polytechnique Fédérale de Lausanne; SuizaFil: Schulte Merker, Stefan. Westfälische Wilhelms Universität; AlemaniaFil: Morelli, Luis Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigación en Biomedicina de Buenos Aires - Instituto Partner de la Sociedad Max Planck; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Institut Max Planck fur Molekulare Physiologie; Alemani