Autonomous oscillators in systems biology are often mathematically expressed as regulatory network models. These models are interrogated to predict oscillator behavior under various environmental conditions. The potential suite of dynamical behaviors arising from a regulatory network model is rich and varied, as one might expect of a complex system. Therefore, a mathematical model has the capability to predict previously unobserved biological oscillator behavior that arises under untested conditions. We present a computational method that describes the full suite of dynamical behaviors of a network model, enabling both mechanistic understanding of experimental observations and prediction of unexpected dynamics. These ideas are presented through example network models, including some relevant to the yeast cell cycle.

Rhythms and oscillations are widely observed in biological systems. However, it is unclear how such noisy systems can produce robust and consistent timing, or how individual molecules or time-keeping systems couple together to produce macroscopically observable rhythms. Here, we focus on the synchronization of oscillatory processes at different scales: from the sub-cellular to the cellular and intercellular levels. Using examples from the circadian rhythms in cyanobacteria, cell cycle in eukaryotes, the firing of neurons, and from other emerging findings on the frontier of autonomous clocks, we discuss different paradigms of coupling or entrainment. We then highlight different methods of analysis from deterministic to stochastic approaches. Specifically, we discuss methods to quantify synchronization and its possible physical mechanisms, as well as prevailing mathematical models. Lastly, we close with a discussion of suggestions for new experiments or theoretical investigation.

Engineering proteins that can switch between states is of strong interest to biotechnology. These include multi-state transcription factors, membrane receptors, kinases, and synthetic molecular logic gates. While traditional directed evolution approaches excel at optimizing steady-state protein functionalities, they require substantial adaptation to treat transitions in states of proteins. This chapter describes how the emerging regulatory logic of autonomous biological oscillators can be used to impose time-varying selection pressure for evolving switchable proteins. We first review the challenges of evolving switchable proteins and examine past strategies, including fluorescence-activated cell sorting (FACS) screens, alternating chemical selection and counterselection methods, and phage display techniques. We then compare these with "optovolution," an approach recently developed by our lab, which couples a protein's activity to host cell cycle progression and leverages programmable light inputs to drive continuous evolution of proteins. To this end, we explain the design principles underlying the use of an autonomous oscillator for evolution and how it promotes selection for both "on" and "off" states, as well as switching between them. In a direct comparison with a conventional directed evolution method, we elucidate how optovolution proves more reliable by avoiding evolutionary routes that hinder counterselection. In conclusion we discuss how optovolution opens new avenues for creating proteins with complex logic and dynamic control, complementing latest advances in computational protein design.

Cell-free extracts have proven to be a tremendous tool for studying cell cycle regulation. This chapter reviews recent advances that expand upon this platform by incorporating synthetic cell-like compartments to encapsulate functional cell cycle regulators. These synthetic approaches allow for a programmable reconstitution of self-sustained autonomous oscillators, including that of mitosis, exhibiting a diverse range of biochemical and physical properties. The high throughput and manipulability of this system provide a comprehensive tool to systematically analyze the single-cell dynamics of this autonomous cell-cycle oscillator across broader yet finer-grained parametric, temporal, and spatial scales. We highlight key applications from the past few years and demonstrate how extending the well-established extract-based research with synthetic systems opens new avenues for tackling unexplored questions regarding cell cycle oscillations and their emergent phenomena.

The nuclear factor κB (NF-κB) signaling pathway plays a crucial role in regulating immune responses, inflammation, and cell survival. After the discovery of NF-κB by Ranjan Sen and David Baltimore as a nuclear factor that binds near the κ light-chain gene in activated B-cells [1], extensive research has been conducted to uncover key biochemical mechanisms underlying the pathway and the downstream genes regulated by NF-κB. The core regulatory module of NF-κB/IκB (inhibitor of NF-κB)/IKK (IκB kinase) has also been a leading example of cell signaling pathways that can produce oscillatory activities, particularly in response to the pro-inflammatory cytokine tumor necrosis factor α (TNF-α). Despite this status, the existence and function of NF-κB oscillations was a contentious topic in the early years. In this chapter, we touch on the history, progression, and outlook of the quest to decipher the properties and biological function of NF-κB oscillations.

The central dogma of molecular biology, which delineates the flow of genetic information from DNA to RNA to proteins, is fundamental to cellular identity and functionality. This process involves intricate steps of transcription, mRNA processing, translation, and protein processing, each of which has been studied extensively over the past decades. Despite significant advancements in our understanding of these individual steps, the mechanisms by which these processes are spatiotemporally coordinated within each cell remain elusive. Efficient and precise transfer of genetic information is critical; any disruptions or "traffic jams" along this pathway including cryptic transcription, aberrant mRNA splicing, ribosome stalling, and protein misfolding and aggregation can lead to severe consequences such as aging and various diseases. Recently, our group has unveiled a cell-autonomous 12-h clock in mammalian cells that modulates the rhythmic activity of the entire genetic information flow. This discovery challenges the existing paradigm that genetic information flow is functioning at steady state but rather suggests that it oscillates with a robust 12-h cycle under normal physiological conditions, peaking at times of transition at dawn and dusk when metabolic stress is heightened. In this chapter, I will delve into the regulation, function, and evolutionary origins of the 12-h clock, and further elaborate how the 12-h clock can be utilized as a discovery tool to uncover hidden principles governing the spatiotemporal coordination of genetic information flow. Special attention will be given to the role of phase separation in facilitating this coordination, highlighting its significance in ensuring the seamless flow of genetic information across various cellular compartments and organelles.

Circadian rhythms have traditionally been considered to be outputs of genetic transcription-translation feedback loop (TTFL) oscillators. However, the discovery of circadian peroxiredoxin oxidation rhythms in anucleate red blood cells suggests that cells also possess an autonomous circadian redox rhythm. The conservation of this rhythm across all lineages of life, as well as in TTFL-defective backgrounds in multiple organisms, further indicates its importance. Rather than functioning as an isolated system, the redox rhythm is bidirectionally coupled to the genetic circadian clock. Perturbation of one oscillation may alter amplitude or shift period of the other, depending on biological context. In animals, the interplay between the redox rhythm and the genetic clock is complex, and the biological significance of the redox oscillation has yet to be established. In plants, immune-related redox perturbation by salicylic acid can reinforce the genetic clock, while the redox rhythm itself gates immune-induced programmed cell death toward morning as a circadian output. We propose that the redox rhythm reflects an intrinsic metabolic cycling in which cells alternate between the high-metabolic states that generate energy, reducing power, and reactive oxygen species (ROS), and the lower-metabolic states that favor detoxification, repair, and restoration of redox homeostasis. In this model, the redox rhythm is driven by the feedback between glycolysis, pentose phosphate pathway, ROS production via electron transport chains, antioxidant capacity, and cellular repair, and becomes entrained to the external cues via diurnal energy generation such as photosynthesis in green lineages.

Repurposing extant resources is at the basis of functional innovation in evolution. In cell biology, conserved regulatory circuits, with minor adjustments to a subset of components, can be recruited for functional novelty. A prominent example concerns multiciliated cells that generate cilia-based fluid flows, vital for organism development and homeostasis. During their post-mitotic differentiation, these cells repurpose the autonomous oscillators that normally govern the cell division cycle to drive massive production of cilia-nucleating organelles, named centrioles, in the cytoplasm without committing to cell division. In this chapter, we review recent advances in understanding how a repurposed cell cycle machinery regulates these cytoplasmic dynamics essential for motile ciliogenesis.

Centrioles are cytoskeletal organelles whose duplication must occur with high temporal precision to ensure faithful cell division, ciliogenesis and tissue organization. Traditionally, the centriole biogenesis cycle has been viewed as a surrogate to the nuclear division cycle, particularly to oscillations in cyclin-dependent kinase (CDK) activity. In this chapter, we revisit classic experimental observations demonstrating that centriole duplication can proceed independently of DNA replication, transcription and CDK oscillations, thereby revealing an intrinsic autonomy in this cycle. We then discuss emerging molecular evidence identifying oscillatory dynamics of Polo-like kinase 4 (Plk4) as the core autonomous clock mechanism that initiates and times centriole biogenesis. Building on this framework, we examine mechanisms that entrain or couple the centriole cycle to the mitotic cycle, ciliogenesis and circadian rhythms, highlighting shared regulatory modules such as ubiquitin ligases and phosphatases. We explore the physiological importance of maintaining proper coupling between these cycles through examples of cancer pathologies and developmental defects that arise when centriole timing becomes uncoupled. Finally, we outline outstanding questions regarding the temporal machinery that governs the centriole biogenesis cycle, its evolution, and emerging therapeutic opportunities, positioning this cycle as a model system for understanding how autonomous cellular clocks integrate into broader temporal control programmes in biology.

Models of the central oscillating mechanism of the cell-division cycle have evolved over more than 40 years of investigation across multiple model systems. The initial oscillator models were based on observations from early embryonic systems and suggested that oscillations were driven by a small biochemical feedback loop comprised of mitotic cyclin, cyclin-dependent kinase (CDK) and the ubiquitin ligase complex, anaphase promoting complex/cyclosome (APC/C). The model was expanded to include kinase and phosphatase regulators of CDK (Wee1 and Cdc25) with experiments in Xenopus extracts. Biochemical models were supported by genetic studies in both S. cerevisiae and S. pombe systems where cell-cycle arrests were associated with mutations in the kinases, phosphatases, and ubiquitin ligases of the cell-cycle clock. Mathematical models also supported these biochemical oscillator models and were able to accurately predict the outcome of genetic experiments. Thus, there was no apparent need for new models until work showed that autonomous cell-cycle oscillations continued when mitotic cyclins were deleted in S. cerevisiae. The advent of transcriptomics technologies in the late 1990s revealed the existence of large programs of oscillating gene expression associated with cell-cycle progression. It was further shown that these programs of oscillating gene expression could function autonomously in S. cerevisiae mutants where mitotic cyclins were disrupted and cell-cycle progression was halted. Taken together, these new findings suggested that a gene regulatory network (GRN) may function as the underlying cell-cycle oscillator with CDKs serving primarily as the effectors of these oscillations. Here, we explore the evolution of these models from early biochemical to more contemporary GRN models.

Embryogenesis begins with fertilization, resulting in a totipotent zygote that undergoes a complex series of cellular and molecular events toward the development of a complete organism. During this period, critical events such as zygotic genome activation and cell fate specification occur, characterized by dynamic changes in gene expression programs. Regulation of gene expression is generally explained by chromatin-based mechanisms orchestrated in nuclei. To note, non-chromatin nuclear proteins, referred to as nucleoskeletal proteins, emerge as key players for shaping nuclear and chromatin structures. The nucleoskeleton consists of multiple proteins, and its dynamics are important for establishing cell-type-specific nuclear structure, genome organization, and gene expression patterns. Recent studies have highlighted that nucleoskeletal proteins, particularly lamins and nuclear actin, play diverse and critical roles during early embryogenesis. Furthermore, a growing body of evidence suggests that nuclear architecture itself can actively influence gene expression and embryonic development. In this review, we focus on the nuclear structure of early vertebrate embryos from the viewpoint of the nucleoskeleton. We summarize current findings regarding the dynamics and functions of nucleoskeletal proteins during embryogenesis and further discuss how these constitutional components can affect gene expression and developmental programs.

Time is an important physical factor controlling all biological phenomena. Within the short period from fertilization to preimplantation, various events occur in a timely manner. A rapid replication of the genome and extensive epigenetic reprogramming occur concomitantly during the transformation from gametes to totipotent zygotes and differentiated cells. In the nuclei, large-scale changes such as genome replication and chromosome segregation progress within a short time. Simultaneously, classical epigenetic information, including histone modifications and DNA methylation patterns, is dynamically remodeled. During this period, the genome, including chromatin architecture and nuclear positioning of gene loci, is under strict control. Recently, single-cell omics analyses and high-throughput chromosome conformation capture (Hi-C) data have provided locus-level resolution of these genomic structures. These global changes inside and outside the cell nuclei occur across several species; however, differences in timing exist because of interspecies variation in developmental speed. In this chapter, we describe the history of research on these spatiotemporal changes inside and outside cell nuclei and present live-cell imaging technology as an important tool for the quantitative analysis of these phenomena.

Early mammalian development entails one of the most extensive and physiologically relevant episodes of epigenomic reprogramming. Following fertilization, two highly specialized gametic epigenomes are reset to establish a totipotent zygotic state and are subsequently reorganized to enable lineage specification and pluripotency. A central component of this transition is the dynamic regulation of histone modifications that mark transcriptionally active and inactive chromatin. Studies in mouse embryos have revealed a distinctive sequence of events in which noncanonical, oocyte- and embryo-specific chromatin states are transiently established and then progressively replaced by canonical, somatic-like patterns around zygotic genome activation. However, comparative analyses across mammals demonstrate that several of these features, including broad noncanonical histone domains and Polycomb-mediated imprinting, are not universally conserved and differ substantially in humans and other species. In this chapter, we summarize recent findings on the dynamics of active and inactive histone marks during early embryogenesis, with a focus on principles derived from the mouse model and their limitations. We discuss how histone modifications contribute to transcriptional competence, repression, and lineage priming, how these processes vary across species, and how they together constitute an epigenomic "rebooting" that balances the erasure of parental memory with the preservation of essential regulatory information.

Faithful chromosome segregation in oocytes relies on the precise coordination of core centromeric chromatin, dynamic kinetochore assembly, and spindle interactions. In meiosis I, sister kinetochores are mono-oriented toward the same spindle pole, allowing homologous chromosomes to bi-orient and segregate properly, whereas meiosis II exhibits conventional bi-orientation of sister chromatids. Stepwise assembly of kinetochore subcomplexes, Meikin-mediated mono-orientation, and protection of centromeric cohesion by Shugoshin ensure accurate segregation through meiotic divisions. These same structural and regulatory features, however, are also exploited by selfish centromeres to bias chromosome orientation on the oocyte spindle, leading to biased segregation to the egg and therefore to the next generation in violation of Mendel's Law of Segregation. We will review recent studies that have established a mechanistic framework for both accurate chromosome segregation and non-Mendelian segregation in oocytes, highlighting the central role of meiotic centromeres in female reproduction and evolutionary conflict.

In metazoans, gametogenesis produces the only cell type capable of transmitting both genetic and epigenetic information to offspring. This process represents one of the most extensive cellular differentiation programs, often originating from germline stem cells (GSCs), as in the female and male Drosophila and C. elegans gonads. These well-defined, unipotent germline lineages provide powerful in vivo models to study epigenetic regulation in multicellular organisms. During gametogenesis, epigenetic mechanisms balance cell differentiation and cellular plasticity. This review summarizes recent findings on how asymmetric sister chromatids are established and segregated during GSC division, the initial step of gametogenesis essential for reproduction in Drosophila and C. elegans. We focus on histones, a major carrier of epigenetic information, and discuss how their inheritance is regulated during GSC asymmetric divisions. Canonical histones and histone variants are dynamically incorporated into chromatin in a cell cycle- and genomic locus-specific manner, and these chromosome-bound epigenetic differences must coordinate with the mitotic machinery to ensure their proper partitioning. Finally, we speculate how these mechanisms may extend beyond the germline, assessing their conservation across species. Understanding these processes provides critical insights into how misregulation contributes to disease and how targeted manipulation could promote tissue homeostasis and regeneration.