Christoph Schmal

• Dr. rer. nat.
• Researcher at Humboldt-Universität zu Berlin

Lymphocytes circulate through lymph nodes (LN) in search for antigen in what is believed to be a continuous process. Here, we show that lymphocyte migration through lymph nodes and lymph occurred in a non-continuous, circadian manner. Lymphocyte homing to lymph nodes peaked at night onset, with cells leaving the tissue during the day. This resulted...

Modern imaging techniques allow the monitoring of circadian rhythms of single cells. Coupling between these single cellular circadian oscillators can generate coherent periodic signals on the tissue level that subsequently orchestrate physiological outputs. The strength of coupling in such systems of oscillators is often unclear. In particular, eff...

Mammalian circadian clocks have a hierarchical organization, governed by the suprachiasmatic nucleus (SCN) in the hypothalamus. The brain itself contains multiple loci that maintain autonomous circadian rhythmicity, but the contribution of the non-SCN clocks to this hierarchy remains unclear. We examine circadian oscillations of clock gene expressi...

Circadian rhythms are generated by interlocked transcriptional-translational negative feedback loops (TTFLs), the molecular process implemented within a cell. The contributions, weighting and balancing between the multiple feedback loops remain debated. Dissociated, free-running dynamics in the expression of distinct clock genes has been described...

Entrainment denotes a process of coordinating the internal circadian clock to external rhythmic time-cues (Zeitgeber), mainly light. It is facilitated by stronger Zeitgeber signals and smaller period differences between the internal clock and the external Zeitgeber. The phase of entrainment ψ is a result of this process on the side of the circadian...

Animal vocalizations comprise a rich array of complex sounds that exhibit nonlinear phenomena (NLP), which have fascinated researchers for decades. From the melodic songs of birds to the clicks and whistles of dolphins, many species have been found to produce nonlinear vocalizations, offering a valuable perspective on the mechanisms underlying soun...

The circadian clock regulates key physiological processes, including cellular responses to DNA damage. Circadian-based therapeutic strategies optimize treatment timing to enhance drug efficacy and minimize side effects, offering potential for precision cancer treatment. However, applying these strategies in cancer remains limited due to a lack of u...

The circadian clock regulates key physiological processes, including cellular responses to DNA damage. Circadian-based therapeutic strategies optimize treatment timing to enhance drug efficacy and minimize side effects, offering potential for precision cancer treatment. However, applying these strategies in cancer remains limited due to limited und...

The circadian clock, a fundamental biological regulator, governs essential cellular processes in health and disease. Circadian-based therapeutic strategies are increasingly gaining recognition as promising avenues. Aligning drug administration with the circadian rhythm can enhance treatment efficacy and minimize side effects. Yet, uncovering the op...

Three parameters are important to characterize a circadian and in general any biological clock: period, phase and amplitude. While circadian periods have been shown to correlate with entrainment phases, and clock amplitude influences the phase response of an oscillator to pulse-like zeitgeber signals, the co-modulations of amplitude and periods, wh...

Circadian clocks are endogenous oscillators present in almost all cells that drive daily rhythms in physiology and behavior. There are two mechanisms that have been proposed to explain how circadian rhythms are generated in mammalian cells: through a transcription-translation feedback loop (TTFL) and based on oxidation/reduction reactions, both of...

The importance of RNA‐binding proteins (RBPs) for plant responses to environmental stimuli and development is well documented. Insights into the portfolio of RNAs they recognize, however, clearly lack behind the understanding gathered in non‐plant model organisms. Here, we characterize binding of the circadian clock‐regulated Arabidopsis thaliana G...

The circadian clock, a fundamental biological regulator, governs essential cellular processes in health and disease. Circadian-based therapeutic strategies are increasingly gaining recognition as promising avenues. Aligning drug administration with the circadian rhythm can enhance treatment efficacy and minimize side effects. Yet, uncovering the op...

The synchronization of multiple oscillators serves as the central mechanism for maintaining stable circadian rhythms in physiology and behavior. Aging and disease can disrupt synchronization, leading to changes in the periodicity of circadian activities. While our understanding of the circadian clock under synchronization has advanced significantly...

Circadian clocks are internal timing devices that have evolved as an adaption to the omnipresent natural 24 h rhythmicity of daylight intensity. Properties of the circadian system are photoperiod dependent. The phase of entrainment varies systematically with season. Plastic photoperiod-dependent re-arrangements in the mammalian circadian core pacem...

Three parameters are important to characterize a circadian and in general any biological clock: period, phase and amplitude. While circadian periods have been shown to correlate with entrainment phases, and clock amplitude influences the phase response of an oscillator to pulse-like zeitgeber signals, the co-modulations of amplitude and periods, wh...

A defining property of circadian clocks is temperature compensation, characterized by the resilience of their near 24-hour free-running periods against changes in environmental temperature within the physiological range. While temperature compensation is evolutionary conserved across different taxa of life and has been studied within many model org...

Three parameters are important to characterize a circadian and in general any biological clock: period, phase and amplitude. While circadian periods have been shown to correlate with entrainment phases, and clock amplitude influences the phase response of an oscillator to pulse-like zeitgeber signals, the co-modulations of amplitude and periods, wh...

Circadian clocks are internal timing devices that have evolved as an adaption to the omnipresent natural 24h rhythmicity of daylight intensity. Properties of the circadian system are photoperiod dependent. The phase of entrainment varies systematically with season. Plastic photoperiod dependent re-arrangements in the mammalian circadian core pacema...

Circadian clocks are endogenous oscillators present in almost all cells that drive daily rhythms in physiology and behavior. There are two mechanisms that have been proposed to explain how circadian rhythms are generated in mammalian cells: through a transcription-translation feedback loop (TTFL) and based on oxidation/reduction reactions, both of...

Experiments that compare rhythmic properties across different genetic alterations and entrainment conditions underlie some of the most important breakthroughs in circadian biology. A robust estimation of the rhythmic properties of the circadian signals goes hand in hand with these discoveries. Widely applied traditional signal analysis methods such...

A defining property of circadian clocks is temperature compensation, characterized by the resilience of circadian free-running periods against changes in environmental temperature. As an underlying mechanism, the balance or critical reaction hypothesis have been proposed. While the former supposes a temperature-dependent balancing of reactions with...

Autonomously oscillating circadian clocks resonate with daily environmental (zeitgeber) rhythms to organize physiology around the solar day. While entrainment properties and mechanisms have been studied widely and in great detail for light-dark cycles, entrainment to daily temperature rhythms remains poorly understood despite that they are potent z...

Clock genes Cry1 and Cry2, inhibitory components of core molecular feedback loop, are regarded as critical molecules for the circadian rhythm generation in mammals. A double knockout of Cry1 and Cry2 abolishes the circadian behavioral rhythm in adult mice under constant darkness. However, robust circadian rhythms in PER2::LUC expression are detecte...

Experiments that compare rhythmic properties across different genetic alterations and entrainment conditions underlie some of the most important breakthroughs in circadian biology. A robust estimation of the rhythmic properties of the circadian signals goes hand in hand with these discoveries. Widely applied traditional signal analysis methods such...

Autonomously oscillating circadian clocks resonate with daily environmental (zeitgeber) rhythms to organize physiology around the solar day. While entrainment properties and mechanisms have been studied widely and in great detail for light-dark cycles, entrainment to daily temperature rhythms remains poorly understood despite that they are potent z...

The mammalian circadian clock is well-known to be important for our sleep–wake cycles, as well as other daily rhythms such as temperature regulation, hormone release or feeding–fasting cycles. Under normal conditions, these daily cyclic events follow 24 h limit cycle oscillations, but under some circumstances, more complex nonlinear phenomena, such...

Methods for the quantification of rhythmic biological signals have been essential for the discovery of function and design of biological oscillators. Advances in live measurements have allowed recordings of unprecedented resolution revealing a new world of complex heterogeneous oscillations with multiple noisy non-stationary features. However, our...

Understanding entrainment of circadian rhythms is a central goal of chronobiology. Many factors, such as period, amplitude, Zeitgeber strength, and daylength, govern entrainment ranges and phases of entrainment. We have tested whether simple amplitude-phase models can provide insight into the control of entrainment phases. Using global optimization...

Mathematical models of varying complexity have helped shed light on different aspects of circadian clock function. In this work, we question whether minimal clock models (Goodwin models) are sufficient to reproduce essential phenotypes of the clock: a small phase response curve (PRC), fast jetlag and seasonal phase shifts. Instead of building a sin...

Understanding entrainment of circadian rhythms is a central goal of chronobiology. Many factors, such as period, amplitude, Zeitgeber strength, and day-length, govern entrainment ranges and the phase of entrainment. Using global optimization, we derive conceptual models with just three free parameters (period, amplitude, relaxation rate) that repro...

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Mathematical models of varying complexity have helped shed light on different aspects of circadian clock function. In this work, we question whether minimal clock models (Goodwin models) are sufficient to reproduce essential phenotypes of the clock: a small phase response curve (PRC), fast jetlag and seasonal phase shifts. Instead of building a sin...

Circadian rhythms are generated by interlocked transcriptional-translational negative feedback loops (TTFLs), the molecular process implemented within a cell. The contributions, weighting and balancing between the multiple feedback loops remain debated. Dissociated, free-running dynamics in the expression of distinct clock genes has been described...

Created on Mathematica 11 in 2016. Output formatting and period estimation requires PMTAnalysis.m package, available at GitHub, SourceForge, and ResearchGate. Relevant figure legend: Fig. 3 g–i The twist coupling model recaptures the acceleration of the circadian oscillation and increase in amplitude by coupling. In the simulation, results from fi...

Motivation: Neural activities of the brain occur through the formation of spatio-temporal patterns. In recent years, macroscopic neural imaging techniques have produced a large body of data on these patterned activities, yet a numerical measure of spatio-temporal coherence has often been reduced to the global order parameter, which does not uncove...

Movie showing the circadian migration of lymphocytes through lymph nodes. At night onset, increased homing due to higher amounts of lymphocyte CCR7 leads to enhanced lymphocyte counts in the lymph node. During the day, higher S1pr1 expression induces the egression of lymphocytes into efferent lymph. Related to Figure 6.

Background The analysis of circadian leaf movement rhythms is a simple yet effective method to study effects of treatments or gene mutations on the circadian clock of plants. Currently, leaf movements are analysed using time lapse photography and subsequent bioinformatics analyses of leaf movements. Programs that are used for this purpose either ar...

In addition to being endogenous, a circadian system must be able to communicate with the outside world and align its rhythmicity to the environment. As a result of such alignment, external Zeitgebers can entrain the circadian system. Entrainment expresses itself in coinciding periods of the circadian oscillator and the Zeitgeber and a stationary ph...

In addition to being endogenous, a circadian system must be able to communicate with the outside world and align its rhythmicity to the environment. As a result of such alignment, external Zeitgebers can entrain the circadian system. Entrainment expresses itself in coinciding periods of the circadian oscillator and the Zeitgeber and a stationary ph...

Circadian clocks are endogenous timekeepers that produce oscillations with a period of about one day. Their rhythmicity originates from complex gene regulatory networks at the cellular level. In the last decades, computational models have been proven to be a powerful tool in order to understand the dynamics and design principles of the complex regu...

Simulations of the “best” parameter set, obtained via the full parameter space sampling-procedure, fit the experimental time traces worse (for a comparison, see Figure 3 A). Blue: Simulated AtGRP7 mRNA oscillations. Green: “COL_LDHH” experimental data set from the DIURNAL database, as used for Figure 3 A. The time traces were normalized to their ma...

A) Detailed description of the cost function. B) Analysis of the one-component posttranscriptional feedback loop. C) Search for self-sustained oscillations. D) Search for noise-induced oscillations. (PDF)

A gradual decrease of the (alternative) splicing coefficient , which accounts for the negative auto-regulation of AtGRP7, shifts the phases of the AtGRP7 mRNA oscillations (A) and of the pre-mRNA oscillations (B) to a later time of day. On top of that, the peaks of the oscillations get increasingly broader. (TIFF)

Dashed: Simulations for the optimal parameter set from Table 1, identical to those of Figure 2. Solid: Even if one adopts for AtGRP8 the same parameters as for AtGRP7 (see Table 1), apart from the constants connected to alternative splicing ( and ) and transcription kinetics (, , and ), the mRNA oscillations of AtGRP7 and AtGRP8 still behave qualit...

One parameter bifurcation diagrams of the maximal transcription rates (left) and (right), corresponding to the dashed lines in Figure 4 A/C/D. The protein concentration values and for stable fixed points are plotted in red and blue, respectively. Protein concentrations for unstable fixed points are kept in black. Dashed lines indicate the parameter...

Function (see Text S1 A) is plotted versus different peak-trough-values . The peak-trough-values and , each leading to a cost function contribution of one, are indicated by vertical dashed lines. (TIFF)

Simulations of the LHY overexpression (LHY-ox) mutant (A), ztl (B), and toc1 (D) null mutants as well as a hypothetical toc1 mutant (C), where the repression of PRR9 by TOC1 is neglected, as described in [11]. Dashed lines denote the wild type (wt) and continuous lines denote the mutant simulations of AtGRP7 mRNA (green) and LHY/CCA1 protein oscill...

Analogously to Figures 4 C/D of the main text, we plotted the color-coded fixed point concentrations of the AtGRP7 pre-mRNA (A) and mRNA (B) as well as the AtGRP8 pre-mRNA (C) and mRNA (D) in the monostable areas of the – bifurcation diagram. The intersection of the dashed lines marks the optimal parameter set from Table 1. (TIFF)

Four key features of the model dynamics (1)–(6) under 12h∶12h LD conditions for the optimal parameter set from Table 1 (Ranking) and for the 19 next best parameter sets (Ranking) resulting from the above described two-step optimization process with random initialization and subsequent evolutionary optimization. A) Two representative examples of the...

A) & B) In silico half-life experiments for AtGRP7 (A) and AtGRP8 (B) mRNA following an experimental protocol (see main text and Text S1 A). In our model, the mRNA and protein half-lives were shown to depend on the day-time at which transcription or translation were stopped, respectively. The dark-blue and red lines denote the same AtGRP7 and AtGRP...

Solid: Reproduction of the results for and from Figure 2. Dashed: Corresponding results after replacing the original core oscillator model from [11] by the refined model from [13] and adapting the activation coefficients according to and . (TIFF)

The circadian clock controls many physiological processes in higher plants and causes a large fraction of the genome to be expressed with a 24h rhythm. The transcripts encoding the RNA-binding proteins AtGRP7 (Arabidopsis thaliana Glycine Rich Protein 7) and AtGRP8 oscillate with evening peaks. The circadian clock components CCA1 and LHY negatively...

We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the probability that the dynamics return to the reliable trajectory after a perturbation of the state of a single nod...