Enhanced entrainability of genetic oscillators by period mismatch

Biological oscillators coordinate individual cellular components so that they function coherently and collectively. They are typically composed of multiple feedback loops, and period mismatch is unavoidable in biological implementations. We investigated the advantageous effect of this period mismatch in terms of a synchronization response to external stimuli. Specifically, we considered two fundamental models of genetic circuits: smooth- and relaxation oscillators. Using phase reduction and Floquet multipliers, we numerically analyzed their entrainability under different coupling strengths and period ratios. We found that a period mismatch induces better entrainment in both types of oscillator; the enhancement occurs in the vicinity of the bifurcation on their limit cycles. In the smooth oscillator, the optimal period ratio for the enhancement coincides with the experimentally observed ratio, which suggests biological exploitation of the period mismatch. Although the origin of multiple feedback loops is often explained as a passive mechanism to ensure robustness against perturbation, we study the active benefits of the period mismatch, which include increasing the efficiency of the genetic oscillators. Our findings show a qualitatively different perspective for both the inherent advantages of multiple loops and their essentiality.Comment: 28 pages, 13 figure

Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems

Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for phase-response curves, a fundamental one-dimensional phase reduction of oscillator models. The proposed theoretical and numerical analysis tools are illustrated on several system-theoretic questions and models arising in the biology of cellular rhythms

Modeling Light Adaptation in Circadian Clock: Prediction of the Response That Stabilizes Entrainment

Periods of biological clocks are close to but often different from the rotation period of the earth. Thus, the clocks of organisms must be adjusted to synchronize with day-night cycles. The primary signal that adjusts the clocks is light. In Neurospora, light transiently up-regulates the expression of specific clock genes. This molecular response to light is called light adaptation. Does light adaptation occur in other organisms? Using published experimental data, we first estimated the time course of the up-regulation rate of gene expression by light. Intriguingly, the estimated up-regulation rate was transient during light period in mice as well as Neurospora. Next, we constructed a computational model to consider how light adaptation had an effect on the entrainment of circadian oscillation to 24-h light-dark cycles. We found that cellular oscillations are more likely to be destabilized without light adaption especially when light intensity is very high. From the present results, we predict that the instability of circadian oscillations under 24-h light-dark cycles can be experimentally observed if light adaptation is altered. We conclude that the functional consequence of light adaptation is to increase the adjustability to 24-h light-dark cycles and then adapt to fluctuating environments in nature

Switching between oscillations and homeostasis in competing negative and positive feedback motifs

We analyze a class of network motifs in which a short, two-node positive feed- back motif is inserted in a three-node negative feedback loop. We demonstrate that such networks can undergo a bifurcation to a state where a stable fixed point and a stable limit cycle coexist. At the bifurcation point the period of the oscillations diverges. Further, intrinsic noise can make the system switch between oscillatory state and the stationary state spontaneously. We find that this switching also occurs in previous models of circadian clocks that use this combination of positive and negative feedback. Our results suggest that real- life circadian systems may need specific regulation to prevent or minimize such switching events.Comment: 8 figure

Synchronization and entrainment of coupled circadian oscillators

Circadian rhythms in mammals are controlled by the neurons located in the suprachiasmatic nucleus of the hypothalamus. In physiological conditions, the system of neurons is very efficiently entrained by the 24-hour light-dark cycle. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light dark cycle in neuronal synchronization. Nevertheless, heterogeneity as a natural and permanent ingredient of these cellular interactions is seemingly to play a major role in these biochemical processes. In this paper we use a model that considers the neurons of the suprachiasmatic nucleus as chemically-coupled modified Goodwin oscillators, and introduce non-negligible heterogeneity in the periods of all neurons in the form of quenched noise. The system response to the light-dark cycle periodicity is studied as a function of the interneuronal coupling strength, external forcing amplitude and neuronal heterogeneity. Our results indicate that the right amount of heterogeneity helps the extended system to respond globally in a more coherent way to the external forcing. Our proposed mechanism for neuronal synchronization under external periodic forcing is based on heterogeneity-induced oscillators death, damped oscillators being more entrainable by the external forcing than the self-oscillating neurons with different periods.Comment: 17 pages, 7 figure

Entrainment dynamics organised by global manifolds in a circadian pacemaker model

This is the final version. Available on open access from Frontiers Media via the DOI in this recordCircadian rhythms are established by the entrainment of our intrinsic body clock to periodic forcing signals provided by the external environment, primarily variation in light intensity across the day/night cycle. Loss of entrainment can cause a multitude of physiological difficulties associated with misalignment of circadian rhythms, including insomnia, excessive daytime sleepiness, gastrointestinal disturbances, and general malaise. This can occur after travel to different time zones, known as jet lag; when changing shift work patterns; or if the period of an individual’s body clock is too far from the 24-hour period of environmental cycles. We consider the loss of entrainment and the dynamics of re-entrainment in a two-dimensional variant of the Forger-Jewett-Kronauer model of the human circadian pacemaker forced by a 24-hour light/dark cycle. We explore the loss of entrainment by continuing bifurcations of one-to-one entrained orbits under variation of forcing parameters and the intrinsic clock period. We show that the severity of the loss of entrainment is dependent on the type of bifurcation inducing the change of stability of the entrained orbit, which is in turn dependent on the environmental light intensity. We further show that for certain perturbations, the model pblackicts a counter-intuitive rapid re-entrainment if the light intensity is sufficiently high. We explain this phenomenon via computation of invariant manifolds of fixed points of a 24-hour stroboscopic map and show how the manifolds organise re-entrainment times following transitions between day and night shift work.Medical Research Council (MRC)US-UK Fulbright CommissionEngineering and Physical Sciences Research Council (EPSRC)National Science Foundation (NSF

Complex and unexpected dynamics in simple genetic regulatory networks

Peer reviewedPublisher PD

Network analysis of complex biological systems : boundedness of weakly reversible chemical reaction networks and conditions for synchronisation of coupled oscillators

Imperial Users onl