Jae Kyoung Kim

Emergent genetic oscillations in a synthetic microbial consortium

Engineering cell population behavior Attaining the full promise of synthetic biology will require designing population-level behaviors of multiple interacting cell types. As a start, Chen et al. engineered two strains of the bacterium Escherichia coli to produce signaling molecules that regulate transcription in the complementary strain (see the Perspective by Teague and Weiss). The signaling circuit was successfully designed to produce feedback loops that produce synchronous oscillations in transcription between the two strains. A mathematical model helped determine how to modulate the oscillations and control their robustness to perturbations. Science, this issue p. 986; see also p. 924 Two strains of bacteria are designed to synchronize transcription in culture. [Also see Perspective by Teague and Weiss] A challenge of synthetic biology is the creation of cooperative microbial systems that exhibit population-level behaviors. Such systems use cellular signaling mechanisms to regulate gene expression across multiple cell types. We describe the construction of a synthetic microbial consortium consisting of two distinct cell types—an “activator” strain and a “repressor” strain. These strains produced two orthogonal cell-signaling molecules that regulate gene expression within a synthetic circuit spanning both strains. The two strains generated emergent, population-level oscillations only when cultured together. Certain network topologies of the two-strain circuit were better at maintaining robust oscillations than others. The ability to program population-level dynamics through the genetic engineering of multiple cooperative strains points the way toward engineering complex synthetic tissues and organs with multiple cell types.

A mechanism for robust circadian timekeeping via stoichiometric balance

Circadian (∼24 h) timekeeping is essential for the lives of many organisms. To understand the biochemical mechanisms of this timekeeping, we have developed a detailed mathematical model of the mammalian circadian clock. Our model can accurately predict diverse experimental data including the phenotypes of mutations or knockdown of clock genes as well as the time courses and relative expression of clock transcripts and proteins. Using this model, we show how a universal motif of circadian timekeeping, where repressors tightly bind activators rather than directly binding to DNA, can generate oscillations when activators and repressors are in stoichiometric balance. Furthermore, we find that an additional slow negative feedback loop preserves this stoichiometric balance and maintains timekeeping with a fixed period. The role of this mechanism in generating robust rhythms is validated by analysis of a simple and general model and a previous model of the Drosophila circadian clock. We propose a double‐negative feedback loop design for biological clocks whose period needs to be tightly regulated even with large changes in gene dosage.

A Novel Protein, CHRONO, Functions as a Core Component of the Mammalian Circadian Clock

Two independent studies, one of them using a computational approach, identified CHRONO, a gene shown to modulate the activity of circadian transcription factors and alter circadian behavior in mice.

Mechanisms That Enhance Sustainability of p53 Pulses

The tumor suppressor p53 protein shows various dynamic responses depending on the types and extent of cellular stresses. In particular, in response to DNA damage induced by γ-irradiation, cells generate a series of p53 pulses. Recent research has shown the importance of sustaining repeated p53 pulses for recovery from DNA damage. However, far too little attention has been paid to understanding how cells can sustain p53 pulses given the complexities of genetic heterogeneity and intrinsic noise. Here, we explore potential molecular mechanisms that enhance the sustainability of p53 pulses by developing a new mathematical model of the p53 regulatory system. This model can reproduce many experimental results that describe the dynamics of p53 pulses. By simulating the model both deterministically and stochastically, we found three potential mechanisms that improve the sustainability of p53 pulses: 1) the recently identified positive feedback loop between p53 and Rorα allows cells to sustain p53 pulses with high amplitude over a wide range of conditions, 2) intrinsic noise can often prevent the dampening of p53 pulses even after mutations, and 3) coupling of p53 pulses in neighboring cells via cytochrome-c significantly reduces the chance of failure in sustaining p53 pulses in the presence of heterogeneity among cells. Finally, in light of these results, we propose testable experiments that can reveal important mechanisms underlying p53 dynamics.

The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.

Modeling and Validating Chronic Pharmacological Manipulation of Circadian Rhythms

Circadian rhythms can be entrained by a light‐dark (LD) cycle and can also be reset pharmacologically, for example, by the CK1δ/ε inhibitor PF‐670462. Here, we determine how these two independent signals affect circadian timekeeping from the molecular to the behavioral level. By developing a systems pharmacology model, we predict and experimentally validate that chronic CK1δ/ε inhibition during the earlier hours of a LD cycle can produce a constant stable delay of rhythm. However, chronic dosing later during the day, or in the presence of longer light intervals, is not predicted to yield an entrained rhythm. We also propose a simple method based on phase response curves (PRCs) that predicts the effects of a LD cycle and chronic dosing of a circadian drug. This work indicates that dosing timing and environmental signals must be carefully considered for accurate pharmacological manipulation of circadian phase.

Protein sequestration versus Hill-type repression in circadian clock models.

Circadian (∼24 h) clocks are self-sustained endogenous oscillators with which organisms keep track of daily and seasonal time. Circadian clocks frequently rely on interlocked transcriptional-translational feedback loops to generate rhythms that are robust against intrinsic and extrinsic perturbations. To investigate the dynamics and mechanisms of the intracellular feedback loops in circadian clocks, a number of mathematical models have been developed. The majority of the models use Hill functions to describe transcriptional repression in a way that is similar to the Goodwin model. Recently, a new class of models with protein sequestration-based repression has been introduced. Here, the author discusses how this new class of models differs dramatically from those based on Hill-type repression in several fundamental aspects: conditions for rhythm generation, robust network designs and the periods of coupled oscillators. Consistently, these fundamental properties of circadian clocks also differ among Neurospora, Drosophila, and mammals depending on their key transcriptional repression mechanisms (Hill-type repression or protein sequestration). Based on both theoretical and experimental studies, this review highlights the importance of careful modelling of transcriptional repression mechanisms in molecular circadian clocks.

A tunable artificial circadian clock in clock-defective mice.

Self-sustaining oscillations are essential for diverse physiological functions such as the cell cycle, insulin secretion and circadian rhythms. Synthetic oscillators using biochemical feedback circuits have been generated in cell culture. These synthetic systems provide important insight into design principles for biological oscillators, but have limited similarity to physiological pathways. Here we report the generation of an artificial, mammalian circadian clock in vivo, capable of generating robust, tunable circadian rhythms. In mice deficient in Per1 and Per2 genes (thus lacking circadian rhythms), we artificially generate PER2 rhythms and restore circadian sleep/wake cycles with an inducible Per2 transgene. Our artificial clock is tunable as the period and phase of the rhythms can be modulated predictably. This feature, and other design principles of our work, might enhance the study and treatment of circadian dysfunction and broader aspects of physiology involving biological oscillators.

Model-driven experimental approach reveals the complex regulatory distribution of p53 by the circadian factor Period 2

Significance Cells sense changes in environmental conditions and translate them into physiological responses that are mediated by a plethora of molecular intermediaries that converge at critical nodes. This is particularly relevant to multiple levels of biological organization in which the circadian clock and cell division are interlocked. Unexpectedly, the circadian rhythms of two critical components of the interlocked system, Period 2 (Per2) and p53, were in antiphase. This finding was analyzed using a systematic modeling approach, and predictions of the model were validated by experimental studies that revealed a distinct and complex scenario. Accordingly, we show that the spatiotemporal organization of Per2:p53 interactions and the nature of their chemical modifications are critical for their time-dependent subcellular redistribution and potential biological functions. The circadian clock and cell cycle networks are interlocked on the molecular level, with the core clock loop exerting a multilevel regulatory role over cell cycle components. This is particularly relevant to the circadian factor Period 2 (Per2), which modulates the stability of the tumor suppressor p53 in unstressed cells and transcriptional activity in response to genotoxic stress. Per2 binding prevents Mdm2-mediated ubiquitination of p53 and, therefore, its degradation, and oscillations in the peaks of Per2 and p53 were expected to correspond. However, our findings showed that Per2 and p53 rhythms were significantly out-of-phase relative to each other in cell lysates and in purified cytoplasmic fractions. These seemingly conflicting experimental data motivated the use of a combined theoretical and experimental approach focusing on the role played by Per2 in dictating the phase of p53 oscillations. Systematic modeling of all possible regulatory scenarios predicted that the observed phase relationship between Per2 and p53 could be simulated if (i) p53 was more stable in the nucleus than in the cytoplasm, (ii) Per2 associates to various ubiquitinated forms of p53, and (iii) Per2 mediated p53 nuclear import. These predictions were supported by a sevenfold increase in p53’s half-life in the nucleus and by in vitro binding of Per2 to the various ubiquitinated forms of p53. Last, p53’s nuclear shuttling was significantly favored by ectopic expression of Per2 and reduced because of Per2 down-regulation. Our combined theoretical/mathematical approach reveals how clock regulatory nodes can be inferred from oscillating time course data.

The relationship between stochastic and deterministic quasi-steady state approximations

BackgroundThe quasi steady-state approximation (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is accurate. However, a number of recent examples show that this is not necessarily the case.ResultsHere we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is accurate whenever its deterministic counterpart provides an accurate approximation over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations.ConclusionsThe stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are accurate. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.