Two-component genetic switch as a synthetic module with tunable stability

Generalized Michaelis-Menten rate law with time-varying molecular concentrations

The Michaelis-Menten (MM) rate law has been the dominant paradigm of modeling biochemical rate processes for over a century with applications in biochemistry, biophysics, cell biology, systems biology, and chemical engineering. The MM rate law and its remedied form stand on the assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium (quasi-steady state) much faster than the molecular concentrations change. Yet, this assumption is not always justified. Here, we relax this quasi-steady state requirement and propose the generalized MM rate law for the interactions of molecules with active concentration changes over time. Our approach for time-varying molecular concentrations, termed the effective time-delay scheme (ETS), is based on rigorously estimated time-delay effects in molecular complex formation. With particularly marked improvements in protein-protein and protein-DNA interaction modeling, the ETS provides an analytical framework to interpret and predict rich transient or rhythmic dynamics (such as autogenously-regulated cellular adaptation and circadian protein turnover), which goes beyond the quasi-steady state assumption.

Cost-effective circadian mechanism: rhythmic degradation of circadian proteins spontaneously emerges without rhythmic post-translational regulation

Circadian protein oscillations are maintained by the lifelong repetition of protein production and degradation in daily balance. It comes at the cost of ever-replayed, futile protein synthesis each day. This biosynthetic cost with a given oscillatory protein profile is relievable by a rhythmic, not constant, degradation rate that selectively peaks at the right time of day but remains low elsewhere, saving much of the gross protein loss and of the replenishing protein synthesis. Here, our mathematical modeling reveals that the rhythmic degradation rate of proteins with circadian production spontaneously emerges under steady and limited activity of proteolytic mediators and does not necessarily require rhythmic post-translational regulation of previous focus. Additional (yet steady) post-translational modifications in a proteolytic pathway can further facilitate the degradation's rhythmicity in favor of the biosynthetic cost saving. Our work is supported by animal and plant circadian data, offering a generic mechanism for potentially widespread, time-dependent protein turnover.

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Rhythmic degradation of circadian proteins lowers the cost of protein synthesis

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This rhythmic degradation emerges without rhythmic post-translational regulation

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Extra, yet steady post-translational modifications enhance degradation rhythmicity

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This mechanism hints at how organisms afford the price of daily biological rhythms

Selected heterozygosity at cis-regulatory sequences increases the expression homogeneity of a cell population in humans

Background

Examples of heterozygote advantage in humans are scarce and limited to protein-coding sequences. Here, we attempt a genome-wide functional inference of advantageous heterozygosity at cis-regulatory regions.

Results

The single-nucleotide polymorphisms bearing the signatures of balancing selection are enriched in active cis-regulatory regions of immune cells and epithelial cells, the latter of which provide barrier function and innate immunity. Examples associated with ancient trans-specific balancing selection are also discovered. Allelic imbalance in chromatin accessibility and divergence in transcription factor motif sequences indicate that these balanced polymorphisms cause distinct regulatory variation. However, a majority of these variants show no association with the expression level of the target gene. Instead, single-cell experimental data for gene expression and chromatin accessibility demonstrate that heterozygous sequences can lower cell-to-cell variability in proportion to selection strengths. This negative correlation is more pronounced for highly expressed genes and consistently observed when using different data and methods. Based on mathematical modeling, we hypothesize that extrinsic noise from fluctuations in transcription factor activity may be amplified in homozygotes, whereas it is buffered in heterozygotes. While high expression levels are coupled with intrinsic noise reduction, regulatory heterozygosity can contribute to the suppression of extrinsic noise.

Conclusions

This mechanism may confer a selective advantage by increasing cell population homogeneity and thereby enhancing the collective action of the cells, especially of those involved in the defense systems in humans.

Electronic supplementary material

The online version of this article (doi:10.1186/s13059-016-1027-8) contains supplementary material, which is available to authorized users.

Hypothetical biomolecular probe based on a genetic switch with tunable symmetry and stability

Background

Genetic switches are ubiquitous in nature, frequently associated with the control of cellular functions and developmental programs. In the realm of synthetic biology, it is of great interest to engineer genetic circuits that can change their mode of operation from monostable to bistable, or even to multistable, based on the experimental fine-tuning of readily accessible parameters. In order to successfully design robust, bistable synthetic circuits to be used as biomolecular probes, or understand modes of operation of such naturally occurring circuits, we must identify parameters that are key in determining their characteristics.

Results

Here, we analyze the bistability properties of a general, asymmetric genetic toggle switch based on a chemical-reaction kinetic description. By making appropriate approximations, we are able to reduce the system to two coupled differential equations. Their deterministic stability analysis and stochastic numerical simulations are in excellent agreement. Drawing upon this general framework, we develop a model of an experimentally realized asymmetric bistable genetic switch based on the LacI and TetR repressors. By varying the concentrations of two synthetic inducers, doxycycline and isopropyl β-D-1-thiogalactopyranoside, we predict that it will be possible to repeatedly fine-tune the mode of operation of this genetic switch from monostable to bistable, as well as the switching rates over many orders of magnitude, in an experimental setting. Furthermore, we find that the shape and size of the bistability region is closely connected with plasmid copy number.

Conclusions

Based on our numerical calculations of the LacI-TetR asymmetric bistable switch phase diagram, we propose a generic work-flow for developing and applying biomolecular probes: Their initial state of operation should be specified by controlling inducer concentrations, and dilution due to cellular division would turn the probes into memory devices in which information could be preserved over multiple generations. Additionally, insights from our analysis of the LacI-TetR system suggest that this particular system is readily available to be employed in this kind of probe.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0279-y) contains supplementary material, which is available to authorized users.

Roles of factorial noise in inducing bimodal gene expression

Some gene regulatory systems can exhibit bimodal distributions of mRNA or protein although the deterministic counterparts are monostable. This noise-induced bimodality is an interesting phenomenon and has important biological implications, but it is unclear how different sources of expression noise (each source creates so-called factorial noise that is defined as a component of the total noise) contribute separately to this stochastic bimodality. Here we consider a minimal model of gene regulation, which is monostable in the deterministic case. Although simple, this system contains factorial noise of two main kinds: promoter noise due to switching between gene states and transcriptional (or translational) noise due to synthesis and degradation of mRNA (or protein). To better trace the roles of factorial noise in inducing bimodality, we also analyze two limit models, continuous and adiabatic approximations, apart from the exact model. We show that in the case of slow gene switching, the continuous model where only promoter noise is considered can exhibit bimodality; in the case of fast switching, the adiabatic model where only transcriptional or translational noise is considered can also exhibit bimodality but the exact model cannot; and in other cases, both promoter noise and transcriptional or translational noise can cooperatively induce bimodality. Since slow gene switching and large protein copy numbers are characteristics of eukaryotic cells, whereas fast gene switching and small protein copy numbers are characteristics of prokaryotic cells, we infer that eukaryotic stochastic bimodality is induced mainly by promoter noise, whereas prokaryotic stochastic bimodality is induced primarily by transcriptional or translational noise.

Building synthetic memory

Cellular memory - conversion of a transient signal into a sustained response - is a common feature of biological systems. Synthetic biologists aim to understand and re-engineer such systems in a reliable and predictable manner. Synthetic memory circuits have been designed and built in vitro and in vivo based on diverse mechanisms, such as oligonucleotide hybridization, recombination, transcription, phosphorylation, and RNA editing. Thus far, building these circuits has helped us explore the basic principles required for stable memory and ask novel biological questions. Here we discuss strategies for building synthetic memory circuits, their use as research tools, and future applications of these devices in medicine and industry.

Delay-managed tradeoff in the molecular dynamics of the segmentation clock

The molecular segmentation clock is a complex regulatory network that governs the periodic somite segmentation in vertebrate embryos. Underlying the rhythm of the segmentation clock is a single-cell level pace-making circuit, where inevitable molecular noise and time delay impose normal operating constraints to the pace-making. However, how the molecular mechanisms of the core circuit of the segmentation clock coordinate the operating constraints and maintain the rhythmic nature of the developmental process remains poorly understood. To address this question, we construct two biologically-motivated mathematical models with multiple clock protein transcription binding sites, with differential or rate-limited decay rates for protein monomers and dimers. We demonstrate that the rate-limited decay significantly enlarges the parameter space of noise-induced and delay-induced oscillations. Interestingly, focusing on the stochastic characters of noise-induced and delay-induced oscillations in terms of phase coherence and phase averaged amplitude noise in the polar coordinate, we find that there is a delay-managed tradeoff between phase coherence and phase averaged amplitude noise. In particular, the model with both multiple binding sites and rate-limited decay can show regular tunability as the delay increases. Our results indicate that transcriptional and post-translational mechanisms constrain the combined effects of noise and delay on the molecular dynamics of the segmentation clock.

Small-number effects: a third stable state in a genetic bistable toggle switch

A genetic toggle switch was studied experimentally and theoretically. We have found an additional kinetic stable state where all the genes express very lowly, which is predicted to be unstable by dynamical systems theory. It can also stably coexist with the other two known stable states, although this coexistence is forbidden in a deterministic dynamical system. We analyze that this nontrivial phenomenon results from the discrete and fluctuate nature in such a small system, by comparing experimental results with modeling results of exact stochastic simulations and differential equations.

Molecular level dynamics of genetic oscillator--the effect of protein-protein interaction

Uncovering how interactions of a set of molecular components influence the system's dynamic behavior is important for understanding intracellular processes and elucidating design principles, but unfortunately, there are limited efforts for studying this issue. Here, we study the effect of distinct post-translational dynamics controlled by protein dimerization on oscillations in the repressilator. For this, we propose three biologically motivated model scenarios of the repressilator with monomer or dimer being the active form of repressor, and with protein-protein interactions. It is found that the dimer dissociation constant can tune oscillatory regions, frequency and amplitude. Introducing a modified linear noise approximation to evaluate fluctuations of amplitude and period in the oscillatory systems, we show that different dimerization leads to a different effect on period and amplitude in reducing noise. The manipulation of the circuit's biochemical properties provides a practical strategy for designing a robust and tunable oscillator.

Microbial linguistics: perspectives and applications of microbial cell-to-cell communication

Inter-cellular communication via diffusible small molecules is a defining character not only of multicellular forms of life but also of single-celled organisms. A large number of bacterial genes are regulated by the change of chemical milieu mediated by the local population density of its own species or others. The cell density-dependent "autoinducer" molecules regulate the expression of those genes involved in genetic competence, biofilm formation and persistence, virulence, sporulation, bioluminescence, antibiotic production, and many others. Recent innovations in recombinant DNA technology and micro-/nano-fluidics systems render the genetic circuitry responsible for cell-to-cell communication feasible to and malleable via synthetic biological approaches. Here we review the current understanding of the molecular biology of bacterial intercellular communication and the novel experimental protocols and platforms used to investigate this phenomenon. A particular emphasis is given to the genetic regulatory circuits that provide the standard building blocks which constitute the syntax of the biochemical communication network. Thus, this review gives focus to the engineering principles necessary for rewiring bacterial chemo-communication for various applications, ranging from population-level gene expression control to the study of host-pathogen interactions.

Synthetic circuits, devices and modules

The aim of synthetic biology is to design artificial biological systems for novel applications. From an engineering perspective, construction of biological systems of defined functionality in a hierarchical way is fundamental to this emerging field. Here, we highlight some current advances on design of several basic building blocks in synthetic biology including the artificial gene control elements, synthetic circuits and their assemblies into devices and modules. Such engineered basic building blocks largely expand the synthetic toolbox and contribute to our understanding of the underlying design principles of living cells.

The art of reporter proteins in science: past, present and future applications

Starting with the first publication of lacZ gene fusion in 1980, reporter genes have just entered their fourth decade. Initial studies relied on the simple fusion of a promoter or gene with a particular reporter gene of interest. Such constructs were then used to determine the promoter activity under specific conditions or within a given cell or organ. Although this protocol was, and still is, very effective, current research shows a paradigm shift has occurred in the use of reporter systems. With the advent of innovative cloning and synthetic biology techniques and microfluidic/nanodroplet systems, reporter genes and their proteins are now finding themselves used in increasingly intricate and novel applications. For example, researchers have used fluorescent proteins to study biofilm formation and discovered that microchannels develop within the biofilm. Furthermore, there has recently been a "fusion" of art and science; through the construction of genetic circuits and regulatory systems, researchers are using bacteria to "paint" pictures based upon external stimuli. As such, this review will discuss the past and current trends in reporter gene applications as well as some exciting potential applications and models that are being developed based upon these remarkable proteins.

Macroscopic kinetic effect of cell-to-cell variation in biochemical reactions

Genetically identical cells under the same environmental conditions can show strong variations in protein copy numbers due to inherently stochastic events in individual cells. We here develop a theoretical framework to address how variations in enzyme abundance affect the collective kinetics of metabolic reactions observed within a population of cells. Kinetic parameters measured at the cell population level are shown to be systematically deviated from those of single cells, even within populations of homogeneous parameters. Because of these considerations, Michaelis-Menten kinetics can even be inappropriate to apply at the population level. Our findings elucidate a novel origin of discrepancy between in vivo and in vitro kinetics, and offer potential utility for analysis of single-cell metabolomic data.

Genetic noise control via protein oligomerization

BACKGROUND

Gene expression in a cell entails random reaction events occurring over disparate time scales. Thus, molecular noise that often results in phenotypic and population-dynamic consequences sets a fundamental limit to biochemical signaling. While there have been numerous studies correlating the architecture of cellular reaction networks with noise tolerance, only a limited effort has been made to understand the dynamic role of protein-protein interactions.

RESULTS

We have developed a fully stochastic model for the positive feedback control of a single gene, as well as a pair of genes (toggle switch), integrating quantitative results from previous in vivo and in vitro studies. In particular, we explicitly account for the fast binding-unbinding kinetics among proteins, RNA polymerases, and the promoter/operator sequences of DNA. We find that the overall noise-level is reduced and the frequency content of the noise is dramatically shifted to the physiologically irrelevant high-frequency regime in the presence of protein dimerization. This is independent of the choice of monomer or dimer as transcription factor and persists throughout the multiple model topologies considered. For the toggle switch, we additionally find that the presence of a protein dimer, either homodimer or heterodimer, may significantly reduce its random switching rate. Hence, the dimer promotes the robust function of bistable switches by preventing the uninduced (induced) state from randomly being induced (uninduced).

CONCLUSION

The specific binding between regulatory proteins provides a buffer that may prevent the propagation of fluctuations in genetic activity. The capacity of the buffer is a non-monotonic function of association-dissociation rates. Since the protein oligomerization per se does not require extra protein components to be expressed, it provides a basis for the rapid control of intrinsic or extrinsic noise. The stabilization of regulatory circuits and epigenetic memory in general is of direct implications to organism fitness. Our results also suggest possible avenues for the design of synthetic gene circuits with tunable robustness for a wide range of engineering purposes.