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.     

Coupling oscillations and switches in genetic networks

Switches (bistability) and oscillations (limit cycle) are omnipresent in biological networks. Synthetic genetic networks producing bistability and oscillations have been designed and constructed experimentally. However, in real biological systems, regulatory circuits are usually interconnected and the dynamics of those complex networks is often richer than the dynamics of simple modules. Here we couple the genetic Toggle switch and the Repressilator, two prototypic systems exhibiting bistability and oscillations, respectively. We study two types of coupling. In the first type, the bistable switch is under the control of the oscillator. Numerical simulation of this system allows us to determine the conditions under which a periodic switch between the two stable steady states of the Toggle switch occurs. In addition we show how birhythmicity characterized by the coexistence of two stable small-amplitude limit cycles, can easily be obtained in the system. In the second type of coupling, the oscillator is placed under the control of the Toggleswitch. Numerical simulation of this system shows that this construction could for example be exploited to generate a permanent transition from a stable steady state to self-sustained oscillations (and vice versa) after a transient external perturbation. Those results thus describe qualitative dynamical behaviors that can be generated through the coupling of two simple network modules. These results differ from the dynamical properties resulting from interlocked feedback loops systems in which a given variable is involved at the same time in both positive and negative feedbacks. Finally the models described here may be of interest in synthetic biology, as they give hints on how the coupling should be designed to get the required properties.     

Implications of a zinc uptake and transport model

While physicists regularly use mathematical equations to describe natural phenomena, mathematical modeling of biological systems is still not well established and is hampered by communication barriers between experimental and theoretical biologists. In a recent study we developed a mathematical model of zinc uptake and radial transport in Arabidopsis thaliana roots. By refraining from writing many equations in the main text and confining the derivation of formulas to a supplemental file, we attempted to reach both experimentalists and theoreticians likewise. Here, we give a short summary of our results on the accumulation pattern of zinc and the importance of transporter regulation, water flow and geometry. For a better understanding of the dynamics of adaptation to changes in external conditions, we plead for more detailed and frequent measurements. As a new aspect, we analyzed the effect of buffering. Simulations indicate that it dampens oscillations and may therefore play a key role in zinc homeostasis.     

Diffusive coupling can discriminate between similar reaction mechanisms in an allosteric enzyme system

Background  

A central question for the understanding of biological reaction networks is how a particular dynamic behavior, such as bistability or oscillations, is realized at the molecular level. So far this question has been mainly addressed in well-mixed reaction systems which are conveniently described by ordinary differential equations. However, much less is known about how molecular details of a reaction mechanism can affect the dynamics in diffusively coupled systems because the resulting partial differential equations are much more difficult to analyze.     

Internal noise-sustained circadian rhythms in a Drosophila model

Circadian rhythmic processes, mainly regulated by gene expression at the molecular level, have inherent stochasticity. Their robustness or resistance to internal noise has been extensively investigated by most of the previous studies. This work focuses on the constructive roles of internal noise in a reduced Drosophila model, which incorporates negative and positive feedback loops, each with a time delay. It is shown that internal noise sustains reliable oscillations with periods close to 24 h in a region of parameter space, where the deterministic kinetics would evolve to a stable steady state. The amplitudes of noise-sustained oscillations are significantly affected by the variation of internal noise level, and the best performance of the oscillations could be found at an optimal noise intensity, indicating the occurrence of intrinsic coherence resonance. In the oscillatory region of the deterministic model, the coherence of noisy circadian oscillations is suppressed by internal noise, while the period remains nearly constant over a large range of noise intensity, demonstrating robustness of the Drosophila model for circadian rhythms to intrinsic noise. In addition, the effects of time delay in the positive feedback on the oscillations are also investigated. It is found that the time delay could efficiently tune the performance of the noise-sustained oscillations. These results might aid understanding of the exploitation of intracellular noise in biochemical and genetic regulatory systems.     

Electrifying rhythms in plant cells

Physiological oscillations (or rhythms) pervade all spatiotemporal scales of biological organization, either because they perform critical functions or simply because they can arise spontaneously and may be difficult to prevent. Regardless of the case, they reflect regulatory relationships between control points of a given system and offer insights as read-outs of the concerted regulation of a myriad of biological processes. Here we review recent advances in understanding ultradian oscillations (period < 24h) in plant cells, with a special focus on single-cell oscillations. Ion channels are at the center stage due to their involvement in electrical/excitabile phenomena associated with oscillations and cell-cell communication. We highlight the importance of quantitative approaches to measure oscillations in appropriate physiological conditions, which are essential strategies to deal with the complexity of biological rhythms. Future development of optogenetics techniques in plants will further boost research on the role of membrane potential in oscillations and waves across multiple cell types.     

Oscillations in calcium-cyclic AMP control loops form the basis of pacemaker activity and other high frequency biological rhythms.

In this paper theoretical and experimental evidence is presented which indicates that oscillations in internal calcium and cyclic AMP concentrations due to an instability in their common control loops are possible and indeed may be widespread. Further, it is demonstrated that fluctuations in various cellular properties, in particular membrane potential, are a direct consequence of these second messenger oscillations. Given the central importance of calcium and cyclic AMP to the regulation of metabolism, these oscillations would influence most metabolic processes especially rhythmic behaviour. We propose that these oscillations form the basis of several biological rhythms including, potential oscillations in cardiac pacemaker cells, neurones and insulin secreting β-cells, the minute rhythm in smooth muscle, cyclic AMP pulses in Dictyostelium, rhythmical cytoplasmic streaming in Physarum and transepitheliel potential oscillations in Calliphora salivary gland. This model makes possible an explanation of the frequency and amplitude effects of hormones.     

The manipulation of calcium oscillations by harnessing self-organisation

This paper investigates how self-organisation might be harnessed for the manipulation and control of calcium oscillations. Calcium signalling mechanisms are responsible for a number of important functions within biological systems, such as fertilization, secretion, contraction, neuronal signalling and learning. In this paper, calcium oscillations are investigated as a biological periodic process. Within biological systems such periodic behaviour is one of the outcomes from self-organisation. The understanding of periodic processes in living systems can enable more accurate diagnosis and physiologically suitable clinical therapies to be proposed, for diseases such as cancer, epilepsy, cardiac diseases and other dynamic diseases. In this paper these ideas are investigated by means of the calcium-induced calcium release (CICR) model and a number of representative simulations of intra and inter-cellular calcium oscillations are used to illustrate the manipulation and control of these oscillations in normal and pathological situations.     

Approaching the molecular origins of collective dynamics in oscillating cell populations

From flocking birds, to organ generation, to swarming bacterial colonies, biological systems often exhibit collective behaviors. Here, we review recent advances in our understanding of collective dynamics in cell populations. We argue that understanding population-level oscillations requires examining the system under consideration at three different levels of complexity: at the level of isolated cells, homogenous populations, and spatially structured populations. We discuss the experimental and theoretical challenges this poses and highlight how new experimental techniques, when combined with conceptual tools adapted from physics, may help us overcome these challenges.     

An experimentalist's guide to computational modelling of the Min system

Spatio-temporal oscillations of the Min proteins are essential for selecting the cell division site in Escherichia coli. These oscillations are a key example of a biological phenomenon that can only be understood on a systems level rather than on the level of its individual components. Here, we review the key concepts that mathematical modelling has added to our understanding of the Min system. While several different mechanisms have been proposed, in all cases the oscillations emerge from a dynamic instability of a uniform protein distribution. To generate this instability, however, the various mechanisms rely on different features of Min protein interactions and transport. We critically evaluate these mechanisms in light of recent experimental evidence. We also review the effects of fluctuations caused by low cellular concentration of Min proteins, and describe how stochastic effects may potentially influence Min protein dynamics.     

Self-organized protein patterns: The MinCDE and ParABS systems

Self-organized protein patterns are of tremendous importance for biological decision-making processes. Protein patterns have been shown to identify the site of future cell division, establish cell polarity, and organize faithful DNA segregation. Intriguingly, several key concepts of pattern formation and regulation apply to a variety of different protein systems. Herein, we explore recent advances in the understanding of two prokaryotic pattern-forming systems: the MinCDE system, positioning the FtsZ ring precisely at the midcell, and the ParABS system, distributing newly synthesized DNA along with the cell. Despite differences in biological functionality, these two systems have remarkably similar molecular components, mechanisms, and strategies to achieve biological robustness.     

Chaos and evolution

There is growing interest in applying nonlinear methods to evolutionary biology. With good reason: the living world is full of nonlinearities, responsible for steady states, regular oscillations, and chaos in biological systems. Evolutionists may find nonlinear dynamics important in studying short-term dynamics of changes in genotype frequency, and in understanding selection and its constraints. More speculatively, dynamical systems theory may be important because nonlinear fluctuations in some traits may sometimes be favored by selection, and because some long-run patterns of evolutionary change could be described using these methods.     

Synchronization of Spontaneous Active Motility of Hair Cell Bundles

Hair cells of the inner ear exhibit an active process, believed to be crucial for achieving the sensitivity of auditory and vestibular detection. One of the manifestations of the active process is the occurrence of spontaneous hair bundle oscillations in vitro. Hair bundles are coupled by overlying membranes in vivo; hence, explaining the potential role of innate bundle motility in the generation of otoacoustic emissions requires an understanding of the effects of coupling on the active bundle dynamics. We used microbeads to connect small groups of hair cell bundles, using in vitro preparations that maintain their innate oscillations. Our experiments demonstrate robust synchronization of spontaneous oscillations, with either 1:1 or multi-mode phase-locking. The frequency of synchronized oscillation was found to be near the mean of the innate frequencies of individual bundles. Coupling also led to an improved regularity of entrained oscillations, demonstrated by an increase in the quality factor.     

Roles of protein ubiquitination and degradation kinetics in biological oscillations

Protein ubiquitination and degradation play important roles in many biological functions and are associated with many human diseases. It is well known that for biochemical oscillations to occur, proper degradation rates of the participating proteins are needed. In most mathematical models of biochemical reactions, linear degradation kinetics has been used. However, the degradation kinetics in real systems may be nonlinear, and how nonlinear degradation kinetics affects biological oscillations are not well understood. In this study, we first develop a biochemical reaction model of protein ubiquitination and degradation and calculate the degradation rate against the concentration of the free substrate. We show that the protein degradation kinetics mainly follows the Michaelis-Menten formulation with a time delay caused by ubiquitination and deubiquitination. We then study analytically how the Michaelis-Menten degradation kinetics affects the instabilities that lead to oscillations using three generic oscillation models: 1) a positive feedback mediated oscillator; 2) a positive-plus-negative feedback mediated oscillator; and 3) a negative feedback mediated oscillator. In all three cases, nonlinear degradation kinetics promotes oscillations, especially for the negative feedback mediated oscillator, resulting in much larger oscillation amplitudes and slower frequencies than those observed with linear kinetics. However, the time delay due to protein ubiquitination and deubiquitination generally suppresses oscillations, reducing the amplitude and increasing the frequency of the oscillations. These theoretical analyses provide mechanistic insights into the effects of specific proteins in the ubiquitination-proteasome system on biological oscillations.     

The molecular clockwork of a protein-based circadian oscillator

The circadian clock of the cyanobacterium Synechococcuselongatus PCC 7942 is governed by a core oscillator consisting of the proteins KaiA, KaiB, and KaiC. Remarkably, circadian oscillations in the phosphorylation state of KaiC can be reconstituted in a test tube by mixing the three Kai proteins and adenosine triphosphate. The in vitro oscillator provides a well-defined system in which experiments can be combined with mathematical analysis to understand the mechanism of a highly robust biological oscillator. In this Review, we summarize the biochemistry of the Kai proteins and examine models that have been proposed to explain how oscillations emerge from the properties of the oscillator’s constituents.     

Transient resetting: a novel mechanism for synchrony and its biological examples

The study of synchronization in biological systems is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. In this paper, by using simple dynamical systems theory, we present a novel mechanism, named transient resetting, for the synchronization of uncoupled biological oscillators with stimuli. This mechanism not only can unify and extend many existing results on (deterministic and stochastic) stimulus-induced synchrony, but also may actually play an important role in biological rhythms. We argue that transient resetting is a possible mechanism for the synchronization in many biological organisms, which might also be further used in the medical therapy of rhythmic disorders. Examples of the synchronization of neural and circadian oscillators as well as a chaotic neuron model are presented to verify our hypothesis.     

In vivo generation of DNA sequence diversity for cellular barcoding

Heterogeneity is a ubiquitous feature of biological systems. A complete understanding of such systems requires a method for uniquely identifying and tracking individual components and their interactions with each other. We have developed a novel method of uniquely tagging individual cells in vivo with a genetic ‘barcode’ that can be recovered by DNA sequencing. Our method is a two-component system comprised of a genetic barcode cassette whose fragments are shuffled by Rci, a site-specific DNA invertase. The system is highly scalable, with the potential to generate theoretical diversities in the billions. We demonstrate the feasibility of this technique in Escherichia coli. Currently, this method could be employed to track the dynamics of populations of microbes through various bottlenecks. Advances of this method should prove useful in tracking interactions of cells within a network, and/or heterogeneity within complex biological samples.     

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.