Period shift induction by intermittent stimulation in a Drosophila model of PER protein oscillations

Reaction-diffusion systems for spatio-temporal intracellular protein networks: A beginner's guide with two examples

Spatio-temporal dynamics of a variety of proteins is, among other things, regulated by post-translational modifications of these proteins. Such modifications can thus influence stability and biochemical activities of the proteins, activity and stability of their upstream targets within specific signalling pathways. Commonly used mathematical tools for such protein–protein (and/or protein-mRNA) interactions in single cells, namely, Michaelis–Menten and Hill kinetics, yielding a system of ordinary differential equations, are extended here into (non-linear) partial differential equations by taking into account a more realistic spatial representation of the environment where these reactions occur. In the modelling framework under consideration, all interactions occur in a cell divided into two compartments, the nucleus and the cytoplasm, connected by the semipermeable nuclear membrane and bounded by the impermeable cell membrane. Passive transport mechanism, modelled by the so-called Kedem–Katchalsky boundary conditions, is used here to represent migration of species throughout the nuclear membrane. Nonlinear systems of partial differential equations are solved by the semi-implicit Rothe method. Examples of two spatial oscillators are shown. Namely, these are the circadian rhythm for concentration of the FRQ protein in Neurospora crassa and oscillatory dynamics observed in the activation and regulation of the p53 protein following DNA damage in mammalian cells.

Circadian clocks and phosphorylation: Insights from computational modeling

Circadian clocks are based on a molecular mechanism regulated at the transcriptional, translational and post-translational levels. Recent experimental data unravel a complex role of the phosphorylations in these clocks. In mammals, several kinases play differential roles in the regulation of circadian rhythmicity. A dysfunction in the phosphorylation of one clock protein could lead to sleep disorders such as the Familial Advanced Sleep Phase Disorder, FASPS. Moreover, several drugs are targeting kinases of the circadian clocks and can be used in cancer chronotherapy or to treat mood disorders. In Drosophila, recent experimental observations also revealed a complex role of the phosphorylations. Because of its high degree of homology with mammals, the Drosophila system is of particular interest. In the circadian clock of cyanobacteria, an atypical regulatory mechanism is based only on three clock proteins (KaiA, KaiB, KaiC) and ATP and is sufficient to produce robust temperature-compensated circadian oscillations of KaiC phosphorylation. This review will show how computational modeling has become a powerful and useful tool in investigating the regulatory mechanism of circadian clocks, but also how models can give rise to testable predictions or reveal unexpected results.

Phase tracking and restoration of circadian rhythms by model-based optimal control

Periodic cellular processes and especially circadian rhythms governed by the oscillating expression of a set of genes based on feedback regulation by their products have become an important issue in biology and medicine. The central circadian clock is an autonomous biochemical oscillator with a period close to 24 h. Research in chronobiology demonstrated that light stimuli can be used to delay or advance the phase of the oscillator, allowing it to influence the underlying physiological processes. Phase shifting and restoration of altered rhythms can generally be viewed as open-loop control problems that may be used for therapeutic purposes in diseases. A circadian oscillator model of the central clock mechanism is studied for the fruit fly Drosophila and show how model-based mixed-integer optimal control allows for the design of chronomodulated pulse-stimuli schemes achieving circadian rhythm restoration in mutants and optimal phase synchronisation between the clock and its environment.

From circadian rhythms to cancer chronotherapeutics

Mammalian circadian rhythms result from a complex organization involving molecular clocks within nearly all "normal" cells and a dedicated neuroanatomical system, which coordinates the so-called "peripheral oscillators." The core of the central clock system is constituted by the suprachiasmatic nuclei that are located on the floor of the hypothalamus. Our understanding of the mechanisms of circadian rhythm generation and coordination processes has grown rapidly over the past few years. In parallel, we have learnt how to use the predictable changes in cellular metabolism or proliferation along the 24h time scale in order to improve treatment outcome for a variety of diseases, including cancer. The chronotherapeutics of malignant diseases has emerged as a result of a consistent development ranging from experimental, clinical, and technological prerequisites to multicenter clinical trials of chronomodulated delivery schedules. Indeed large dosing-time dependencies characterize the tolerability of anticancer agents in mice or rats, a better efficacy usually results from treatment administration near the least toxic circadian time in rodent tumor models. Programmable in time multichannel pumps have allowed to test the chronotherapy concepts in cancer patients and to implement chronomodulated delivery schedules in current practice. Clinical phase I and II trials have established the feasibility, the safety, and the activity of the chronotherapy schedules, so that this treatment method has undergone further evaluation in international multicenter phase III trials. Overall, more than 2,000 patients with metastatic disease have been registered in chronotherapy trials. Improved tolerability and/or better antitumor activity have been demonstrated in randomized multicenter studies involving large patient cohorts. The relation between circadian rhythmicity and quality of life and even survival has also been a puzzling finding over the recent years. An essential step toward further developments of circadian-timed therapy has been the recent constitution of a Chronotherapy cooperative group within the European Organization for Research and Treatment of Cancer. This group now involves over 40 institutions in 12 countries. It is conducting currently six trials and preparing four new studies. The 19 contributions in this special issue reflect the current status and perspectives of the several components of cancer chronotherapeutics.

Time-patterned drug administration: insights from a modeling approach

The physiological effects of a drug depend not only on its molecular structure but also on the time-pattern of its administration. One of the main reasons for the importance of temporal patterns in drug action is biological rhythms--particularly those of circadian period. These rhythms affect most physiological functions as well as drug metabolism, clearance, and dynamic processes that may alter drug availability and target cell responsiveness with reference to biological time. We present an overview of the importance of time-patterned signals in physiology focused on the insights provided by a modeling approach. We first discuss examples of pulsatile intercellular communication by hormones such as gonadotropin-releasing hormone, and by cyclic adenosine monophosphate (cAMP) signals in Dictyostelium amoebae. Models based on reversible receptor desensitization account in both cases for the existence of optimal patterns of pulsatile signaling. Turning to circadian rhythms, we examine how models can be used to account for the response of 24h patterns to external stimuli such as light pulses or gene expression, and to predict how to restore the physiological characteristics of altered rhythms. Time-patterned treatments of cancer involve two distinct lines of research. The first, currently evaluated in clinical trials, relies on circadian chronomodulation of anticancer drugs, while the second, mostly based on theoretical studies, involves a resonance phenomenon with the cell-cycle length. We discuss the implications of modeling studies to improve the temporal patterning of drug administration.