Background information. Oscillations of cytosolic Ca2+ are well-known to rely on the regulatory properties of the
InsP3R (inositol 1,4,5-trisphosphate receptor). Three isoforms of this channel have been identified. They differ in
their regulatory properties by Ca2+ and InsP3. Experiments in different cell types clearly indicate that the relative
amounts of each isoform affect the time course of Ca2+ changes after agonist stimulation. In the present study,
we investigate whether different steady-state curves for the open probability of the InsP3Rs as a function of Ca2+
imply different dynamical behaviours when these receptors are present in a cellular environment. We therefore
describe by a specific phenomenological model the three main types of curves that have been reported: (i) the
classical bell-shaped curve, (ii) the bell-shaped curve that is shifted towards higher Ca2+ concentrations when
InsP3 is increased, and (iii) a monotonous increasing function of cytosolic Ca2+.
Results. We show that, although these types of curves can be ascribed to slight differences in the channel regulation by Ca2+ and InsP3, they can indicate important variations as to the receptor role in cellular Ca2+ control. Thus the receptor associated with the classical bell-shaped curve appears to be the most robust Ca2+ oscillator. If the steady-state curve is supposed to be a monotonous increasing function of cytosolic Ca2+, the modelled receptor cannot sustain Ca2+ oscillations in the absence of Ca2+ exchanges with the extracellular medium. When the bellshaped curve is shifted towards higher Ca2+ concentrations with increasing InsP3 levels, the model predicts that the receptor is less robust to changes in density; this receptor, however, provides a finer control of the steady-state level of Ca2+ when varying the InsP3 concentration.
Conclusions. Our model allows us to propose an explanation for the experimental observations about the effect of selectively expressing or down-regulating InsP3R isoforms, as well as to make theoretical predictions.
Abstract : A three-variable model describing the oscillatory activity of a cascade of enzyme reactions is analyzed. A quasi-steady-state approximation reduces the three equations to a system of two equations which admits only a stable steady state. This apparent failure of the quasi-steadystate approximation to describe the limit-cycle oscillations observed in the full, three-variable system is analyzed in detail. We first show that the oscillations occur in the full system provided the Michaelis constants are sufficiently small. We then develop a method for determining the correct limit for application of the quasi-steady-state approximation. The leading problem consists of two equations for a conservative oscillator, and a higher order analysis is required in order to determine the amplitude of the limit-cycle oscillations. Finally, we observe a good agreement when comparing exact numerical and approximate bifurcation diagrams.
Abstract : The amoebae Dictyostelium discoideum aggregate after starvation in a wavelike manner in response to periodic pulses of cyclic AMP (cAMP) secreted by cells which behave as aggregation centers. In addition to autonomous oscillations, the cAMP signaling system that controls aggregation is also capable of excitable behavior, which consists in the transient amplification of suprathreshold pulses of extracellular cAMP. Since the first theoretical model for slime mold aggregation proposed by Keller and Segel in 1970, many theoretical studies have addressed various aspects of the mechanism and function of cAMP signaling in Dictyostelium. This paper presents a brief overview of these developments as well as some reminiscences of the authoršs collaboration with Lee Segel in modeling the dynamics of cAMP relay and oscillations. Considered in turn are models for cAMP signaling in Dictyostelium, the developmental path followed by the cAMP signaling system after starvation, the frequency encoding of cAMP signals, and the origin of concentric or spiral waves of cAMP.
Abstract : Circadian rhythms, characterized by a period of about 24 h, are the most widespread biological rhythms generated autonomously at the molecular level. The core molecular mechanism responsible for circadian oscillations relies on the negative regulation exerted by a protein on the expression of its own gene. Deterministic models account for the occurrence of autonomous circadian oscillations, for their entrainment by light-dark cycles, and for their phase shifting by light pulses. Stochastic versions of these models take into consideration the molecular fluctuations that arise when the number of molecules involved in the regulatory mechanism is low. Numerical simulations of the stochastic models show that robust circadian oscillations can already occur with a limited number of mRNA and protein molecules, in the range of a few tens and hundreds, respectively. Various factors affect the robustness of circadian oscillations with respect to molecular noise. Besides an increase in the number of molecules, entrainment by light-dark cycles, and cooperativity in repression enhance robustness, whereas the proximity of a bifurcation point leads to less robust oscillations. Another parameter that appears to be crucial for the coherence of circadian rhythms is the binding/unbinding rate of the inhibitory protein to the promoter of the clock gene. Intercellular coupling further increases the robustness of circadian oscillations.
Abstract : An intriguing property of circadian clocks is that their free-running period is not exactly 24h. Using models for circadian rhythms in Neurospora and Drosophila, we determine how the entrainment of these rhythms is affected by the free-running period and by the amplitude of the external light-dark cycle. We first consider the model for Neurospora, in which light acts by inducing the expression of a clock gene. We show that the amplitude of the oscillations of the clock protein entrained by light-dark cycles is maximized when the free-running period is smaller than 24h. Moreover, if the amplitude of the light-dark cycle is very strong, complex oscillations occur when the free-running period is close to 24h. In the model for circadian rhythms in Drosophila, light acts by enhancing the degradation of a clock protein. We show that while the amplitude of circadian oscillations entrained by light-dark cycles is also maximized if the free-running period is smaller than 24h, the range of entrainment is centered around 24h in this model. We discuss the physiological relevance of these results in regard to the setting of the free-running period of the circadian clock.
Abstract : Circadian rhythms originate from intertwined feedback processes in genetic regulatory networks. Computational models of increasing complexity have been proposed for the molecular mechanism of these rhythms, which occur spontaneously with a period on the order of 24 h. We show that deterministic models for circadian rhythms in Drosophila account for a variety of dynamical properties, such as phase shifting or long-term suppression by light pulses and entrainment by light/dark cycles. Stochastic versions of these models allow us to examine how molecular noise affects the emergence and robustness of circadian oscillations. Finally, we present a deterministic model for the mammalian circadian clock and use it to address the dynamical bases of physiological disorders of the sleep/wake cycle in humans.
Abstract : A comprehensive study is performed on the condition-dependent expression of genes coding for the components of hand curated multi-protein complexes of the yeast Saccharomyces cerevisiae, in order to identify coherent transcriptional modules within these complexes. Such modules are defined as groups of genes within complexes whose expression profiles under a common set of experimental conditions allow us to discriminate them from random sets of genes. Our analysis reveals that complexes such as the cytoplasmic ribosome, the proteasome and the respiration chain complexes previously characterized as "stable" or "permanent" represent transcriptional modules that are coherently up or down-regulated in many different conditions. Overall however, some level of coherent expression is detected only in 71 out of the total of 113 complexes with at least five different protein components that could be reliably analyzed. Of these, 26 behave as coherently expressed transcriptional modules encompassing all the components of the complex. In another 15, at least half of the components make up such modules and in ten, few or no modules are detected. In an additional 20 complexes coherent expression is detected, but in too few conditions to enable reliable module detection. Interestingly, the transcriptional modules, when detected, often correspond to one or more known sub-complexes with specific functions. Furthermore, detected modules are generally consistent with transcriptional modules identified on the basis of predicted cis-regulatory sequence motifs. Also, groups of genes shared between complexes that carry out related functions tend to be part of overlapping transcriptional modules identified in these complexes. Together these findings suggest that transcriptional modules may represent basic functional and evolutionary building blocs of protein complexes.