Complex and unexpected dynamics in simple genetic regulatory networks

Peer reviewedPublisher PD

Synthetic in vitro transcriptional oscillators

The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells

概日時計におけるインターロック逆位相振動子の設計原理

In system biology, mathematical models have long tradition are used to understand complex biological control processes/ systems, for example, circadian clock oscillatory mechanism. Circadian rhythms (~24 hour) is ubiquitous in almost the living species ranging from mammals to cyanobacteria shows the robustness of key oscillatory features such as the phase, period and amplitude against external and internal variations. These autonomous oscillations are formed by the complex interactions of the interactive molecules. A transcriptional-translational feedback loop is typically characterized as a common principle for this sustained oscillations. Recently studies, it has broadly been established that the robustness of biochemical oscillators, like the Drosophila circadian clocks, can be generated by interlocked transcriptional-translational feedback loops, where two negative feedback loops are coupled through mutual activations. The mechanisms by which such coupling protocols have survived out of many possible protocols remain to be revealed. To address this question, we investigated two distinct coupling protocols: activator-coupled oscillators (ACO) and repressor-coupled oscillators (RCO). We focused on the two coupling parameters: coupling dissociation constant and coupling time delay. Interestingly, the ACO was able to produce anti-phase or morning-evening cycles, whereas the RCO produced in-phase ones. Deterministic and stochastic analyses demonstrated that the anti-phase ACO provided greater fluctuations in amplitude not only with respect to changes in coupling parameters but also to random parameter perturbations than the in-phase RCO. Moreover, the ACO deteriorated the entrainability to the day-night master clock, whereas the RCO produced high entrainability. Considering that the real, interlocked feedback loops have evolved as the ACO, instead of the RCO, we first proposed a hypothesis that the morning-evening or anti-phase cycle is more essential for Drosophila than achieving the robustness and entrainability.九州工業大学博士学位論文 学位記番号:情工博甲第352号 学位授与年月日:令和2年9月25日1 BACKGROUND|2 THE DYNAMICS MODELS OF CIRCADIAN RHYTHMS|3 MODELING THE INTERLOCKED NEGATIVE FEEDBACK LOOPS|4 ROBUSTNESS OF THE INTERLOCKED CIRCADIAN OSCILLATORS|5 ENTRAINABILITY OF THE COUPLED OSCILLATORS|6 CONCLUSIONS AND FUTURE WORK九州工業大学令和2年

Temporal metabolic partitioning of the yeast and protist cellular networks:the cell is a global scale-invariant (fractal or self-similar) multioscillator

Britton Chance, electronics expert when a teenager, became an enthusiastic student of biological oscillations, passing on this enthusiasm to many students and colleagues, including one of us (DL). This historical essay traces BC’s influence through the accumulated work of DL to DL’s many collaborators. The overall temporal organization of mass-energy, information, and signaling networks in yeast in self-synchronized continuous cultures represents, until now, the most characterized example of in vivo elucidation of time structure. Continuous online monitoring of dissolved gases by direct measurement (membrane-inlet mass spectrometry, together with NAD(P)H and flavin fluorescence) gives strain-specific dynamic information from timescales of minutes to hours as does two-photon imaging. The predominantly oscillatory behavior of network components becomes evident, with spontaneously synchronized cellular respiration cycles between discrete periods of increased oxygen consumption (oxidative phase) and decreased oxygen consumption (reductive phase). This temperature-compensated ultradian clock provides coordination, linking temporally partitioned functions by direct feedback loops between the energetic and redox state of the cell and its growing ultrastructure. Multioscillatory outputs in dissolved gases with 13 h, 40 min, and 4 min periods gave statistical self-similarity in power spectral and relative dispersional analyses: i.e., complex nonlinear (chaotic) behavior and a functional scale-free (fractal) network operating simultaneously over several timescales

Entrainment in forced Winfree systems

Rhythmic behavior is widely present in living organisms. The rhythms can be innate and usually they are externally stimulated by the environment. One such stimulus is the 24 h natural light-dark cycle which governs the activity-inactivity cycle of many plants, animals and humans. The cells in the suprachiasmatic nucleus that govern our circadian rhythms are ideally regarded as a group of biological oscillators. In the Winfree model, the biological oscillators are regarded as coupled oscillators. The Winfree model was used to describe the synchronization of a large system of globally coupled phase oscillators. Considering that external stimuli and environmental factors, such as the change of light and darkness, have great influence on the rhythmic behavior, a periodic forcing is added to Winfree system. The thesis focuses on a case where the mean natural frequency of the oscillators is the same with the frequency of the external forcing. A simple case is analyzed with the Poincare map for only one forced oscillator. Then through a careful study of synchronized states and stability on identical oscillators, we obtain the entrainment degree. For a more general case, we study the state diagrams of non-identical oscillators whose natural frequencies follow a uniform or a Lorentz distribution. The Ott-Antonsen is used to give a low-dimensional dynamical description of the system. Then we study the case of detuned systems. We investigate the difference between the detuned and non-detuned cases for identical oscillators and understand the entrainment patterns using stability theory

Reconstruction, mobility, and synchronization in complex networks

During the last decades, it has become clear that systems formed by many interacting parts show emergent dynamical properties which are inherently related to the topology of the underlying pattern of connections among the constituent parts. Such systems, usually known as complex systems, are in general suitably described through their networks of contacts, that is, in terms of nodes (representing the system's components) and edges (standing for their interactions), which allows to catch their essential features in a simple and general representation. In recent years, increasing interest on this approach, thanks also to a favorable technological progress, led to the accumulation of an increasing amount of data. This situation has allowed the arising of new questions and, therefore, the diversification of the scientific work. Among them, we can point out three general issues that have been receiving a lot of interest: (i) is the available information always reliable and complete? (ii) how does a complex interaction pattern affect the emergence of collective behavior in complex systems? And (iii) which is the role of mobility within the framework of complex networks? This thesis has been developed along these three lines, which are strictly interrelated. We expand on three case-studies, each one of which deals with two the above mentioned macro-issues. We consider the issue of the incompleteness of the available information both in the case of natural (Chapter 2) and artificial (Chapter 3) networks. As a paradigmatic emergent behavior, we focus on the synchronization of coupled phase oscillators (Chapter 2 and Chapter 4), deeply investigating how different patterns of connections can affect the achievement of a globally coherent state. Finally, we include moving agents in two different frameworks, using them as explorers of unknown networks (Chapter 3) and considering them as interacting units able to establish connections with their neighbors (Chapter 4). In Chapter 2, we study the problem of the reconstruction of an unknown interaction network, whose nodes are Kuramoto oscillators. Our aim is to extract topological features of the connectivity pattern from purely dynamical measures, based on the fact that in a heterogeneous network the global dynamics is not only affected by the distribution of the natural frequencies but also by the location of the different values. The gathered topological information ranges from local features, such as the single node connectivity, to the hierarchical structure of functional clusters, and even to the entire adjacency matrix. In Chapter 4, instead, we present a model of integrate and fire oscillators that are moving agents, freely displacing on a plane. The phase of the oscillators evolves linearly in time and when it reaches a threshold value they fire at their neighbors. In this way, the interaction network is a dynamical object by itself since it is re-created at each time step by the motion of the units. Depending on the velocity of the motion, the average number of neighbors, the coupling strength and the size of the agents population, we identify different regimes. Moving agents are employed also in Chapter 3 where they play the role of explorers of unknown artificial networks, having the mission to recover information about their structures. We propose a model in which random walkers with previously assigned home nodes navigate through the network during a fixed amount of time. We consider that the exploration is successful if the walker gets the information gathered back home, otherwise, no data is retrieved. We show that there is an optimal solution to this problem in terms of the average information retrieved and the degree of the home nodes and design an adaptive strategy based on the behavior of the random walker.Durante las últimas décadas, se ha empezado a poner de manifiesto que sistemas formados por muchos elementos en interacción pueden mostrar propiedades dinámicas emergentes relacionadas con la topología del patrón de conexiones entre las partes constituyentes. Estos sistemas, generalmente conocidos como sistemas complejos, en muchos casos pueden ser descritos a través de sus redes de contactos, es decir, en términos de nodos (que representan los componentes del sistema) y de enlaces (sus interacciones). De esta manera es posible capturar sus características esenciales en una representación simple y general. En esta última década, el creciente interés en este enfoque, gracias también a un progreso tecnológico favorable, ha llevado a la acumulación de una cantidad ingente de datos. Eso, a su vez, ha permitido el surgimiento de nuevas preguntas y, por lo tanto, la diversificación de la actividad científica. Entre ellas, podemos destacar tres cuestiones generales que son objeto de mucho interés: (i) ¿la información disponible es siempre fiable y completa? (ii) ¿cómo un patrón de interacción complejo puede afectar el surgimiento de comportamientos colectivos? Y (iii) ¿cual es el papel de la movilidad en el marco de las redes complejas? Esta tesis se ha desarrollado siguiendo estas tres líneas, que están íntimamente relacionadas entre sí. Hemos profundizado en tres casos de estudio, cada uno de los cuales se ocupa de dos de los macro-temas mencionados. Consideramos la cuestión del carácter incompleto de la información disponible tanto en el caso de redes naturales (Capítulo 2) como de redes artificiales (Capítulo 3). Nos centramos en la sincronización de los osciladores de fase acoplados (Capítulos 2 y 4) en cuanto comportamiento emergente paradigmático, investigando en profundidad cómo los diferentes patrones de conexión puedan afectar la consecución de un estado coherente a nivel global. Por último, analizamos el rol de la movilidad incluyendo agentes móviles en dos marcos diferentes. En un caso, los utilizamos como exploradores de redes desconocidas (Capítulo 3), mientras que en otro los consideramos como unidades que interaccionan y son capaces de establecer conexiones con sus vecinos (Capítulo 4)

Genetic Oscillations and Vertebrate Embryonic Development

Recurrent processes are a general feature of living systems, from the cell cycle to circadian day-night rhythms to hibernation and flowering cycles. During development and life, numerous recurrent processes are controlled by genetic oscillators, a specific class of genetic regulatory networks that generates oscillations in the level of gene products. A vital mechanism controlled by genetic oscillators is the rhythmic and sequential segmentation of the elongating body axis of vertebrate embryos. During this process, a large collection of coupled genetic oscillators gives rise to spatio-temporal wave patterns of oscillating gene expression at tissue level, forming a dynamic prepattern for the precursors of the vertebrae. While such systems of genetic oscillators have been studied extensively over the past years, many fundamental questions about their collective behavior remain unanswered. In this thesis, we study the behavior and the properties of genetic oscillators from the single oscillator scale to the complex pattern forming system involved in vertebrate segmentation. Genetic oscillators are subject to fluctuations because of the stochastic nature of gene expression. To study the effects of noisy biochemical coupling on genetic oscillators, we propose a theory in which both the internal dynamics of the oscillators as well as the coupling process are inherently stochastic. We find that stochastic coupling of oscillators profoundly affects their precision and synchronization properties, key features for their viability as biological pacemakers. Moreover, stochasticity introduces phenomena not known from deterministic systems, such as stochastic switching between different modes of synchrony. During vertebrate segmentation, genetic oscillators play a key role in establishing a segmental prepattern on tissue scale. We study the spatio-temporal patterns of oscillating gene expression using a continuum theory of coupled phase oscillators. We investigate the effects of different biologically relevant factors such as delayed coupling due to complex signaling processes, local tissue growth, and tissue shortening on pattern formation and segmentation. We find that the decreasing tissue length induces a Doppler effect that contributes to the rate of segment formation in a hitherto unanticipated way. Comparison of our theoretical findings with experimental data reveals the occurrence of such a Doppler effect in vivo. To this end, we develop quantification methods for the spatio-temporal patterns of gene expression in developing zebrafish embryos. On a cellular level, tissues have a discrete structure. To study the interplay of cellular processes like cell division and random cell movement with pattern formation, we go beyond the coarse-grained continuum theories and develop a three-dimensional cell-based model of vertebrate segmentation, in which the dynamics of the segmenting tissue emerges from the collective behavior of individual cells. We show that this model is able to describe tissue formation and segmentation in a self-organized way. It provides the first step of theoretically describing pattern formation and tissue dynamics during vertebrate segmentation in a unified framework involving a three-dimensional tissue with cells as distinct mechanical entities. Finally, we study the synchronization dynamics of generic oscillator systems whose coupling is subject to phase shifts and time delays. Such phase shifts and time delays are induced by complex signaling processes as found, e.g., between genetic oscillators. We show how phase shifts and coupling delays can alter the synchronization dynamics while leaving the collective frequency of the synchronized oscillators invariant. We find that in globally coupled systems, fastest synchronization occurs for non-vanishing coupling delays while in spatially extended systems, fastest synchronization can occur on length scales larger than the coupling range, giving rise to novel synchronization scenarios. Beyond their potential relevance for biological systems, these results have implications for general oscillator systems, e.g., in physics and engineering. In summary, we use discrete and continuous theories of genetic oscillators to study their dynamic behavior, comparing our theoretical results to experimental data where available. We cover a wide range of different topics, contributing to the general understanding of genetic oscillators and synchronization and revealing a hitherto unknown mechanism regulating the timing of embryonic pattern formation