The nature of the root clock at single cell resolution: Principles of communication and similarities with plant and animal pulsatile and circadian mechanisms

Oscillatory mechanisms are present in most life forms and regulate biological processes periodically. In multicellular organisms where more than one oscillatory mechanism is present, they are organized forming a hierarchical coordinated system even at the cellular level. Here, we focus on the Root Clock, an oscillatory mechanism located at the tip of roots that patterns the spacing of lateral organs through oscillating gene expression. We present a series of recent findings and hypotheses about the cellular mechanisms driving the oscillations, how oscillatory information is transmitted within this clock and similarities with other oscillatory systems. Next, we review principles of communication in other pulsatile mechanisms such as circadian rhythms in plants and mammals, and address the possible communication between plant circadian rhythms and the Root Clock. Finally, we advocate for the use of single-cell approaches to address cell communication, synchronization and integration of external outputs into the Root Clock system.     

Systems and synthetic biology approaches in understanding biological oscillators

Background: Self-sustained oscillations are a ubiquitous and vital phenomenon in living systems. From primitive single-cellular bacteria to the most sophisticated organisms, periodicities have been observed in a broad spectrum of biological processes such as neuron firing, heart beats, cell cycles, circadian rhythms, etc. Defects in these oscillators can cause diseases from insomnia to cancer. Elucidating their fundamental mechanisms is of great significance to diseases, and yet challenging, due to the complexity and diversity of these oscillators. Results: Approaches in quantitative systems biology and synthetic biology have been most effective by simplifying the systems to contain only the most essential regulators. Here, we will review major progress that has been made in understanding biological oscillators using these approaches. The quantitative systems biology approach allows for identification of the essential components of an oscillator in an endogenous system. The synthetic biology approach makes use of the knowledge to design the simplest, de novo oscillators in both live cells and cell-free systems. These synthetic oscillators are tractable to further detailed analysis and manipulations. Conclusion: With the recent development of biological and computational tools, both approaches have made significant achievements.     

Modeling oscillatory control in NF-κB, p53 and Wnt signaling

Oscillations are commonly observed in cellular behavior and span a wide range of timescales, from seconds in calcium signaling to 24 hours in circadian rhythms. In between lie oscillations with time periods of 1-5 hours seen in NF-κB, p53 and Wnt signaling, which play key roles in the immune system, cell growth/death and embryo development, respectively. In the first part of this article, we provide a brief overview of simple deterministic models of oscillations. In particular, we explain the mechanism of saturated degradation that has been used to model oscillations in the NF-κB, p53 and Wnt systems. The second part deals with the potential physiological role of oscillations. We use the simple models described earlier to explore whether oscillatory signals can encode more information than steady-state signals. We then discuss a few simple genetic circuits that could decode information stored in the average, amplitude or frequency of oscillations. The presence of frequency-detector circuit downstream of NF-κB or p53 would be a strong clue that oscillations are important for the physiological response of these signaling systems.     

Synthetic circuit of inositol phosphorylceramide synthase in Leishmania: a chemical biology approach

Building circuits and studying their behavior in cells is a major goal of systems and synthetic biology. Synthetic biology enables the precise control of cellular states for systems studies, the discovery of novel parts, control strategies, and interactions for the design of robust synthetic systems. To the best of our knowledge, there are no literature reports for the synthetic circuit construction for protozoan parasites. This paper describes the construction of genetic circuit for the targeted enzyme inositol phosphorylceramide synthase belonging to the protozoan parasite Leishmania. To explore the dynamic nature of the circuit designed, simulation was done followed by circuit validation by qualitative and quantitative approaches. The genetic circuit designed for inositol phosphorylceramide synthase (Biomodels Database—MODEL1208030000) shows responsiveness, oscillatory and bistable behavior, together with intrinsic robustness.     

Oscillations by Minimal Bacterial Suicide Circuits Reveal Hidden Facets of Host-Circuit Physiology

Synthetic biology seeks to enable programmed control of cellular behavior though engineered biological systems. These systems typically consist of synthetic circuits that function inside, and interact with, complex host cells possessing pre-existing metabolic and regulatory networks. Nevertheless, while designing systems, a simple well-defined interface between the synthetic gene circuit and the host is frequently assumed. We describe the generation of robust but unexpected oscillations in the densities of bacterium Escherichia coli populations by simple synthetic suicide circuits containing quorum components and a lysis gene. Contrary to design expectations, oscillations required neither the quorum sensing genes (luxR and luxI) nor known regulatory elements in the P_luxI promoter. Instead, oscillations were likely due to density-dependent plasmid amplification that established a population-level negative feedback. A mathematical model based on this mechanism captures the key characteristics of oscillations, and model predictions regarding perturbations to plasmid amplification were experimentally validated. Our results underscore the importance of plasmid copy number and potential impact of “hidden interactions” on the behavior of engineered gene circuits - a major challenge for standardizing biological parts. As synthetic biology grows as a discipline, increasing value may be derived from tools that enable the assessment of parts in their final context.     

Synchronized ATP oscillations have a critical role in prechondrogenic condensation during chondrogenesis

The skeletal elements of embryonic limb are prefigured by prechondrogenic condensation in which secreted molecules such as adhesion molecules and extracellular matrix have crucial roles. However, how the secreted molecules are controlled to organize the condensation remains unclear. In this study, we examined metabolic regulation of secretion in prechondrogenic condensation, using bioluminescent monitoring systems. We here report on ATP oscillations in the early step of chondrogenesis. The ATP oscillations depended on both glycolysis and mitochondrial respiration, and their synchronization among cells were achieved via gap junctions. In addition, the ATP oscillations were driven by Ca²⁺ oscillations and led to oscillatory secretion in chondrogenesis. Blockade of the ATP oscillations prevented cellular condensation. Furthermore, the degree of cellular condensation increased with the frequency of ATP oscillations. We conclude that ATP oscillations have a critical role in prechondrogenic condensation by inducing oscillatory secretion.     

Influence of parameter values on the oscillation sensitivities of two p53–Mdm2 models

Biomolecular networks that present oscillatory behavior are ubiquitous in nature. While some design principles for robust oscillations have been identified, it is not well understood how these oscillations are affected when the kinetic parameters are constantly changing or are not precisely known, as often occurs in cellular environments. Many models of diverse complexity level, for systems such as circadian rhythms, cell cycle or the p53 network, have been proposed. Here we assess the influence of hundreds of different parameter sets on the sensitivities of two configurations of a well-known oscillatory system, the p53 core network. We show that, for both models and all parameter sets, the parameter related to the p53 positive feedback, i.e. self-promotion, is the only one that presents sizeable sensitivities on extrema, periods and delay. Moreover, varying the parameter set values to change the dynamical characteristics of the response is more restricted in the simple model, whereas the complex model shows greater tunability. These results highlight the importance of the presence of specific network patterns, in addition to the role of parameter values, when we want to characterize oscillatory biochemical systems.

Electronic supplementary material

The online version of this article (doi:10.1007/s11693-015-9173-y) contains supplementary material, which is available to authorized users.     

Systems biology as a foundation for genome-scale synthetic biology

As the ambitions of synthetic biology approach genome-scale engineering, comprehensive characterization of cellular systems is required, as well as a means to accurately model cell-scale molecular interactions. These requirements are coincident with the goals of systems biology and, thus, systems biology will become the foundation for genome-scale synthetic biology. Systems biology will form this foundation through its efforts to reconstruct and integrate cellular systems, develop the mathematics, theory and software tools for the accurate modeling of these integrated systems, and through evolutionary mechanisms. As genome-scale synthetic biology is so enabled, it will prove to be a positive feedback driver of systems biology by exposing and forcing researchers to confront those aspects of systems biology which are inadequately understood.     

A model cortical circuit for the storage of temporal sequences

Despite the fact that temporal information processing is of particular significance in biological memory systems, not much has yet been explored about how these systems manage to store temporal information involved in sequences of stimuli. A neural network model capable of learning and recalling temporal sequences is proposed, based on a neural mechanism in which the sequences are expanded into a series of periodic rectangular oscillations. Thus, the mathematical framework underlying the model, to some extent, is concerned with the Walsh function series. The oscillatory activities generated by the interplay between excitatory and inhibitory neuron pools are transmitted to another neuron pool whose role in learning and retrieval is to modify the rhythms and phases of the rectangular oscillations. Thus, a basic functional neural circuit involves three different neuron pools. The modifiability of rhythms and phases is incorporated into the model with the aim of improving the quality of the retrieval. Numerical simulations were conducted to show the characteristic features of the learning as well as the performance of the model in memory recall.     

Robust Concentration and Frequency Control in Oscillatory Homeostats

Homeostatic and adaptive control mechanisms are essential for keeping organisms structurally and functionally stable. Integral feedback is a control theoretic concept which has long been known to keep a controlled variable robustly (i.e. perturbation-independent) at a given set-point by feeding the integrated error back into the process that generates . The classical concept of homeostasis as robust regulation within narrow limits is often considered as unsatisfactory and even incompatible with many biological systems which show sustained oscillations, such as circadian rhythms and oscillatory calcium signaling. Nevertheless, there are many similarities between the biological processes which participate in oscillatory mechanisms and classical homeostatic (non-oscillatory) mechanisms. We have investigated whether biological oscillators can show robust homeostatic and adaptive behaviors, and this paper is an attempt to extend the homeostatic concept to include oscillatory conditions. Based on our previously published kinetic conditions on how to generate biochemical models with robust homeostasis we found two properties, which appear to be of general interest concerning oscillatory and homeostatic controlled biological systems. The first one is the ability of these oscillators (“oscillatory homeostats”) to keep the average level of a controlled variable at a defined set-point by involving compensatory changes in frequency and/or amplitude. The second property is the ability to keep the period/frequency of the oscillator tuned within a certain well-defined range. In this paper we highlight mechanisms that lead to these two properties. The biological applications of these findings are discussed using three examples, the homeostatic aspects during oscillatory calcium and p53 signaling, and the involvement of circadian rhythms in homeostatic regulation.     

THE OCCURRENCE AND FUNCTIONS OF ULTRADIAN RHYTHMS

Ultradian oscillations with periods between 5 min and 4 h have been described in cell-free extracts, single-celled eukaryotes, cultured cells and embryos. Whereas some of these potentially oscillatory systems (e.g. glycolysis) may only exhibit this type of behaviour rarely if at all in vivo , other ultradian oscillators in lower eukaryotes are rhythms and probably have timekeeping functions. Rhythms with ultradian periods of 10 min to 20 h in oxygen consumption and carbon dioxide production have also been studied in endotherm animals: these rhythms may be modified by variations of environmental parameters and by circadian and infradian synchronizers. Interspecies and interstrain differences strongly suggest that these rhythms are endogenous and have a genetic origin. We suggest that the temporal organization of biochemical and physiological processes facilitates optimization of thermodynamic maintenance of the organism within the random fluctuations of its physicochemical environment and contributes to genetic selection.     

Collective oscillations in developing cells: insights from simple systems

From hormonal secretion to gene expression, multicellular dynamics are rich in oscillatory regulation. When organized in space and time, periodic cell-cell signaling can give rise to long-range coordination of gene expression and cell movement in tissues. Lack of synchrony of the oscillations on the other hand can serve as a source of initial divergence of cell fate in stem cells. How properties of individual cells can account for collective rhythmic behaviors at the tissue level remains elusive in most cases. Recently, studies in chemical reactions, synthetic gene circuits, yeast and social amoeba Dictyostelium have greatly enhanced our view of collective oscillations in cell populations. From these relatively simple systems, a unified view of how excitable and oscillatory regulations could be tuned and coupled to give rise to tissue-level oscillations is emerging. The review focuses on recent progress in cyclic adenosine monophosphate oscillations in Dictyostelium and highlights similarities and differences with other systems. We will see that the autonomy of single-cell level oscillations and different ways in which cells are coupled influence how group-level information can be encoded in collective oscillations.     

Dynamic Processes in Regulation and Some Implications for Biofeedback and Biobehavioral Interventions

Systems theory has long been used in psychology, biology, and sociology. This paper applies newer methods of control systems modeling for assessing system stability in health and disease. Control systems can be characterized as open or closed systems with feedback loops. Feedback produces oscillatory activity, and the complexity of naturally occurring oscillatory patterns reflects the multiplicity of feedback mechanisms, such that many mechanisms operate simultaneously to control the system. Unstable systems, often associated with poor health, are characterized by absence of oscillation, random noise, or a very simple pattern of oscillation. This modeling approach can be applied to a diverse range of phenomena, including cardiovascular and brain activity, mood and thermal regulation, and social system stability. External system stressors such as disease, psychological stress, injury, or interpersonal conflict may perturb a system, yet simultaneously stimulate oscillatory processes and exercise control mechanisms. Resonance can occur in systems with negative feedback loops, causing high-amplitude oscillations at a single frequency. Resonance effects can be used to strengthen modulatory oscillations, but may obscure other information and control mechanisms, and weaken system stability. Positive as well as negative feedback loops are important for system function and stability. Examples are presented of oscillatory processes in heart rate variability, and regulation of autonomic, thermal, pancreatic and central nervous system processes, as well as in social/organizational systems such as marriages and business organizations. Resonance in negative feedback loops can help stimulate oscillations and exercise control reflexes, but also can deprive the system of important information. Empirical hypotheses derived from this approach are presented, including that moderate stress may enhance health and functioning.     

Concerted simulations reveal how peroxidase compound III formation results in cellular oscillations

A major problem in mathematical modeling of the dynamics of complex biological systems is the frequent lack of knowledge of kinetic parameters. Here, we apply Brownian dynamics simulations, based on protein three-dimensional structures, to estimate a previously undetermined kinetic parameter, which is then used in biochemical network simulations. The peroxidase-oxidase reaction involves many elementary steps and displays oscillatory dynamics important for immune response. Brownian dynamics simulations were performed for three different peroxidases to estimate the rate constant for one of the elementary steps crucial for oscillations in the peroxidase-oxidase reaction, the association of superoxide with peroxidase. Computed second-order rate constants agree well with available experimental data and permit prediction of rate constants at physiological conditions. The simulations show that electrostatic interactions depress the rate of superoxide association with myeloperoxidase, bringing it into the range necessary for oscillatory behavior in activated neutrophils. Such negative electrostatic steering of enzyme-substrate association presents a novel control mechanism and lies in sharp contrast to the electrostatically-steered fast association of superoxide and Cu/Zn superoxide dismutase, which is also simulated here. The results demonstrate the potential of an integrated and concerted application of structure-based simulations and biochemical network simulations in cellular systems biology.