Collective oscillation period of inter-coupled biological negative cyclic feedback oscillators

A number of biological rhythms originate from networks comprised of multiple cellular oscillators. But analytical results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has been reported, may be different from that of an autonomous oscillator. Based on cyclic feedback oscillators, we analyze the collective oscillation pattern of coupled cellular oscillators. First we give a condition under which the oscillator network exhibits oscillatory and synchronized behavior. Then we estimate the collective oscillation period based on a novel multivariable harmonic balance technique. Analytical results are derived in terms of biochemical parameters, thus giving insight into the basic mechanism of biological oscillation and providing guidance in synthetic biology design.Comment: arXiv admin note: substantial text overlap with arXiv:1203.125

Oscillation patterns in negative feedback loops

Organisms are equipped with regulatory systems that display a variety of dynamical behaviours ranging from simple stable steady states, to switching and multistability, to oscillations. Earlier work has shown that oscillations in protein concentrations or gene expression levels are related to the presence of at least one negative feedback loop in the regulatory network. Here we study the dynamics of a very general class of negative feedback loops. Our main result is that in these systems the sequence of maxima and minima of the concentrations is uniquely determined by the topology of the loop and the activating/repressing nature of the interaction between pairs of variables. This allows us to devise an algorithm to reconstruct the topology of oscillating negative feedback loops from their time series; this method applies even when some variables are missing from the data set, or if the time series shows transients, like damped oscillations. We illustrate the relevance and the limits of validity of our method with three examples: p53-Mdm2 oscillations, circadian gene expression in cyanobacteria, and cyclic binding of cofactors at the estrogen-sensitive pS2 promoter.Comment: 10 pages, 8 figure

Oscillations and temporal signalling in cells

The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce oscillations in gene expression or protein concentration, using a framework of simple mathematical models. We focus on three eukaryotic genetic regulatory networks which show "ultradian" oscillations, with time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NFkB). We argue that underlying all three is a common design consisting of a negative feedback loop with time delay which is responsible for the oscillatory behaviour

Rapid cell-free forward engineering of novel genetic ring oscillators

While complex dynamic biological networks control gene expression in all living organisms, the forward engineering of comparable synthetic networks remains challenging. The current paradigm of characterizing synthetic networks in cells results in lengthy design-build-test cycles, minimal data collection, and poor quantitative characterization. Cell-free systems are appealing alternative environments, but it remains questionable whether biological networks behave similarly in cell-free systems and in cells. We characterized in a cell-free system the 'repressilator,' a three-node synthetic oscillator. We then engineered novel three, four, and five-gene ring architectures, from characterization of circuit components to rapid analysis of complete networks. When implemented in cells, our novel 3-node networks produced population-wide oscillations and 95% of 5-node oscillator cells oscillated for up to 72 hours. Oscillation periods in cells matched the cell-free system results for all networks tested. An alternate forward engineering paradigm using cell-free systems can thus accurately capture cellular behavior

Evolutionarily stable and fragile modules of yeast biochemical network

Gene and protein interaction networks have evolved to precisely specify cell fates and functions. Here, we analyse whether the architecture of these networks affects evolvability. We find evidence to suggest that in yeast these networks are mainly acyclic, and that evolutionary changes in these parts do not affect their global dynamic properties. In contrast, feedback loops strongly influence dynamic behaviour and are often evolutionarily conserved. Feedback loops are often found to reside in a clustered manner by means of coupling and nesting with each other in the molecular interaction network of yeast. In these clusters some feedback mechanisms are biologically vital for the operation of the module and some provide auxiliary functional assistance. We find that the biologically vital feedback mechanisms are highly conserved in both transcription regulation and protein interaction network of yeast. In particular, long feedback loops and oscillating modules in protein interaction networks are found to be biologically vital and hence highly conserved. These data suggest that biochemical networks evolve differentially depending on their structure with acyclic parts being permissive to evolution while cyclic parts tend to be conserved

Mathematical models for somite formation

Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite formation. We begin by presenting current experimental information and mechanisms explaining somite formation, highlighting features which will be included in the models. For each model we outline the mathematical basis, show results of numerical simulations, discuss their successes and shortcomings and avenues for future exploration. We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area

Mathematical models for somite formation

Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite formation. We begin by presenting current experimental information and mechanisms explaining somite formation, highlighting features which will be included in the models. For each model we outline the mathematical basis, show results of numerical simulations, discuss their successes and shortcomings and avenues for future exploration. We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area

Reliability of Transcriptional Cycles and the Yeast Cell-Cycle Oscillator

A recently published transcriptional oscillator associated with the yeast cell cycle provides clues and raises questions about the mechanisms underlying autonomous cyclic processes in cells. Unlike other biological and synthetic oscillatory networks in the literature, this one does not seem to rely on a constitutive signal or positive auto-regulation, but rather to operate through stable transmission of a pulse on a slow positive feedback loop that determines its period. We construct a continuous-time Boolean model of this network, which permits the modeling of noise through small fluctuations in the timing of events, and show that it can sustain stable oscillations. Analysis of simpler network models shows how a few building blocks can be arranged to provide stability against fluctuations. Our findings suggest that the transcriptional oscillator in yeast belongs to a new class of biological oscillators