Sources of Variability in a Synthetic Gene Oscillator

Computational modeling establishes mechanotransduction as a potent modulator of the mammalian circadian clock

Mechanotransduction, which is the integration of mechanical signals from the external environment of a cell to changes in intracellular signaling, governs many cellular functions. Recent studies have shown that the mechanical state of the cell is also coupled to the cellular circadian clock. To investigate possible interactions between circadian rhythms and cellular mechanotransduction, we have developed a computational model that integrates the two pathways. We postulated that translocation of the transcriptional regulators MRTF (herein referring to both MRTF-A and MRTF-B), YAP and TAZ (also known as YAP1 and WWTR1, respectively; collectively denoted YAP/TAZ) into the nucleus leads to altered expression of circadian proteins. Simulations from our model predict that lower levels of cytoskeletal activity are associated with longer circadian oscillation periods and higher oscillation amplitudes, which is consistent with recent experimental observations. Furthermore, accumulation of YAP/TAZ and MRTF in the nucleus causes circadian oscillations to decay in our model. These effects hold both at the single-cell level and within a population-level framework. Finally, we investigated the effects of mutations in YAP or lamin A, the latter of which result in a class of diseases known as laminopathies. In silico, oscillations in circadian proteins are substantially weaker in populations of cells with mutations in YAP or lamin A, suggesting that defects in mechanotransduction can disrupt the circadian clock in certain disease states; however, reducing substrate stiffness in the model restores normal oscillatory behavior, suggesting a possible compensatory mechanism. Thus, our study identifies that mechanotransduction could be a potent modulatory cue for cellular clocks and that this crosstalk can be leveraged to rescue the circadian clock in disease states.

Network design principle for robust oscillatory behaviors with respect to biological noise

Oscillatory behaviors, which are ubiquitous in transcriptional regulatory networks, are often subject to inevitable biological noise. Thus, a natural question is how transcriptional regulatory networks can robustly achieve accurate oscillation in the presence of biological noise. Here, we search all two- and three-node transcriptional regulatory network topologies for those robustly capable of accurate oscillation against the parameter variability (extrinsic noise) or stochasticity of chemical reactions (intrinsic noise). We find that, no matter what source of the noise is applied, the topologies containing the repressilator with positive autoregulation show higher robustness of accurate oscillation than those containing the activator-inhibitor oscillator, and additional positive autoregulation enhances the robustness against noise. Nevertheless, the attenuation of different sources of noise is governed by distinct mechanisms: the parameter variability is buffered by the long period, while the stochasticity of chemical reactions is filtered by the high amplitude. Furthermore, we analyze the noise of a synthetic human nuclear factor κB (NF-κB) signaling network by varying three different topologies and verify that the addition of a repressilator to the activator-inhibitor oscillator, which leads to the emergence of high-robustness motif—the repressilator with positive autoregulation—improves the oscillation accuracy in comparison to the topology with only an activator-inhibitor oscillator. These design principles may be applicable to other oscillatory circuits.

Multiple transcription auto regulatory loops can act as robust oscillators and decision-making motifs

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We have shown that:

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Negative transcription auto regulation can speed up the response time at the cost of reduced steady state protein levels. Under strong binding conditions, one can increase the steady state protein level by increasing the gene copy number without a compromise on the response time.

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Multiple negative transcription autoregulatory motifs can be tuned for both the response time as well as steady state protein levels by varying the gene copy number.

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Multiple negative autoregulatory loops can act as robust genetic oscillators.

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Dual feedback motifs constructed with multiple negative and positive autoregulatory loop components can act as robust oscillators and bistable decision making units within the transcription factor networks.

Response time decides how fast a gene can react against an external signal at the transcription level in a signalling cascade. The steady state protein levels of the responding genes decide the coupling between two consecutive members of a signalling cascade. A negative autoregulatory loop (NARL) present in a transcription factor network can speed up the response time of the regulated gene at the cost of reduced steady state protein level. We present here a multi NARL motif which can be tuned for both the steady state protein level as well as response time in the required direction. Remarkably, there exists an optimum Hill coefficient n_opt≅4 at which the response time of the NARL motif is at minimum. When the Hill coefficient is n < n_opt, then under strong binding conditions, one can raise the steady state protein level by increasing the gene copy number with almost no change in the response time of the multi NARL motif. Using detailed computational analysis, we show that the coupled multi NARL and positive auto regulatory loop (PARL) motifs can act as an oscillator as well as decision making component which are robust against extrinsic fluctuations in the control parameters. We further demonstrate that the period of oscillation of the coupled multi NARL-PARL dual feedback oscillator can also be fine-tuned by the gene copy number apart from the inducer concentration. We finally demonstrate robustness of bistable dual feedback decision making motifs with multi autoregulatory loop component.

Context-aware synthetic biology by controller design: Engineering the mammalian cell

The rise of systems biology has ushered a new paradigm: the view of the cell as a system that processes environmental inputs to drive phenotypic outputs. Synthetic biology provides a complementary approach, allowing us to program cell behavior through the addition of synthetic genetic devices into the cellular processor. These devices, and the complex genetic circuits they compose, are engineered using a design-prototype-test cycle, allowing for predictable device performance to be achieved in a context-dependent manner. Within mammalian cells, context effects impact device performance at multiple scales, including the genetic, cellular, and extracellular levels. In order for synthetic genetic devices to achieve predictable behaviors, approaches to overcome context dependence are necessary. Here, we describe control systems approaches for achieving context-aware devices that are robust to context effects. We then consider cell fate programing as a case study to explore the potential impact of context-aware devices for regenerative medicine applications.

Stochastic models coupling gene expression and partitioning in cell division in Escherichia coli

Regulation of future RNA and protein numbers is a key process by which cells continuously best fit the environment. In bacteria, RNA and proteins exist in small numbers and their regulatory processes are stochastic. Consequently, there is cell-to-cell variability in these numbers, even between sister cells. Traditionally, the two most studied sources of this variability are gene expression and RNA and protein degradation, with evidence suggesting that the latter is subject to little regulation, when compared to the former. However, time-lapse microscopy and single molecule fluorescent tagging have produced evidence that cell division can also be a significant source of variability due to asymmetries in the partitioning of RNA and proteins. Relevantly, the impact of this noise differs from noise in production and degradation since, unlike these, it is not continuous. Rather, it occurs at specific time points, at which moment it can introduce major fluctuations. Several models have now been proposed that integrate noise from cell division, in addition to noise in gene expression, to mimic the dynamics of RNA and protein numbers of cell lineages. This is expected to be particularly relevant in genetic circuits, where significant fluctuations in one component protein, at specific time moments, are expected to perturb near-equilibrium states of the circuits, which can have long-lasting consequences. Here we review stochastic models coupling these processes in Escherichia coli, from single genes to small circuits.

Modeling the tunability of the dual-feedback genetic oscillator

Oscillatory gene circuits are ubiquitous to biology and are involved in fundamental processes of cell cycle, circadian rhythms, and developmental systems. The synthesis of small, non-natural oscillatory genetic circuits has been increasingly used to test the fundamental principles of genetic network dynamics. While the "repressilator" was used to first demonstrate the proof of principle, a more recently developed dual-feedback, fast, tunable genetic oscillator has demonstrated a greater degree of robustness and control over oscillatory behavior by combining positive- and negative-feedback loops. This oscillator, combining lacI (negative-) and araC (positive-) feedback loops, was, however, modeled using multiple layers of differential equations to capture the molecular complexity of regulation, in order to explain the experimentally measured oscillations. In the search for design principles of such minimal oscillatory circuits, we have developed a reduced model of this dual-feedback loop oscillator consisting of just six differential equations, two of which are delay differential equations. The delay term is optimized, as the only free parameter, to fit the experimental dynamics of the oscillator period and amplitude tunability by the two inducers isopropyl β-D-1-thiogalactopyranoside (IPTG) and arabinose. We proceed to use our reduced and experimentally validated model to redesign the network by comparing the effect of asymmetry in gene expression at the level of (a) DNA copy numbers and the rates of (b) mRNA translation and (c) degradation, since experimental and theoretical work had predicted a need for an asymmetry in the copy numbers of activator (araC) and repressor (lacI) genes encoded on plasmids. We confirm that the minimal period of the oscillator is sensitive to DNA copy number asymmetry, and can demonstrate that while the asymmetry in the translation rate has an identical effect as the plasmid copy numbers, modulating the asymmetry in mRNA degradation can improve the tunability of the period and amplitude of the oscillator. Thus, our model predicts control at the level of translation can be used to redesign such networks, for improved tunability, while at the same time making the network robust to replication "noise" and the effects of the host cell cycle. Thus, our model predicts experimentally testable principles to redesign a potentially more robust oscillatory genetic network.

Roles of cellular heterogeneity, intrinsic and extrinsic noise in variability of p53 oscillation

The p53 protein is a key mediator of the cellular response to various stress signals. In response to DNA damage, the concentration of p53 can temporally oscillate with fluctuations in both the amplitude and period. The underlying mechanism for p53 variability is not fully understood. Here, we construct a core regulatory network of p53 dynamics comprising the ATM-p53-Wip1 and p53-Mdm2 negative feedback loops. We dissect the contributions of cellular heterogeneity, intrinsic noise, and multiple forms of extrinsic noise to p53 variability in terms of the coefficients of variation of four quantities. Cellular heterogeneity greatly determines the fraction of oscillating cells among a population of isogenic cells. Intrinsic noise-fluctuation in biochemical reactions-has little impact on p53 variability given large amounts of molecules, whereas extrinsic colored noise with proper strength and correlation time contributes much to oscillatory variability in individual cells. With the three sources of noise combined, our results reproduce the experimental observations, suggesting that the long correlation time of colored noise is essential to p53 variability. Compared with previous studies, the current work reveals both the individual and integrated effects of distinct noise sources on p53 variability. This study provides a framework for exploring the variability in oscillations in cellular signaling pathways.

Using time-lapse fluorescence microscopy to study gene regulation

Time-lapse fluorescence microscopy is a powerful tool to study gene regulation. By probing fluorescent signals in single cells over extended period of time, this method can be used to study the dynamics, noise, movement, memory, inheritance, and coordination, of gene expression during cell growth, development, and differentiation. In combination with a flow-cell device, it can also measure gene regulation by external stimuli. Due to the single cell nature and the spatial/temporal capacity, this method can often provide information that is hard to get using other methods. Here, we review the standard experimental procedures and new technical developments in this field.

The Timing of Transcriptional Regulation in Synthetic Gene Circuits

Transcription factors and their target promoters are central to synthetic biology. By arranging these components into novel gene regulatory circuits, synthetic biologists have been able to create a wide variety of phenotypes, including bistable switches, oscillators, and logic gates. However, transcription factors (TFs) do not instantaneously regulate downstream targets. After the gene encoding a TF is turned on, the gene must first be transcribed, the transcripts must be translated, and sufficient TF must accumulate in order to bind operator sites of the target promoter. The time to complete this process, here called the "signaling time," is a critical aspect in the design of dynamic regulatory networks, yet it remains poorly characterized. In this work, we measured the signaling time of two TFs in Escherichia coli commonly used in synthetic biology: the activator AraC and the repressor LacI. We found that signaling times can range from a few to tens of minutes, and are affected by the expression rate of the TF. Our single-cell data also show that the variability of the signaling time increases with its mean. To validate these signaling time measurements, we constructed a two-step genetic cascade, and showed that the signaling time of the full cascade can be predicted from those of its constituent steps. These results provide concrete estimates for the time scales of transcriptional regulation in living cells, which are important for understanding the dynamics of synthetic transcriptional gene circuits.

Elements of biological oscillations in time and space

Oscillations in time and space are ubiquitous in nature and play critical roles in dynamic cellular processes. Although the molecular mechanisms underlying the generation of the dynamics are diverse, several distinct regulatory elements have been recognized as being critical in producing and modulating oscillatory dynamics. These include negative and positive feedback, time delay, nonlinearity in regulation, and random fluctuations ('noise'). Here we discuss the specific roles of these five elements in promoting or attenuating oscillatory dynamics, by drawing on insights from quantitative analyses of natural or synthetic biological networks.

Effects of cell cycle noise on excitable gene circuits

We assess the impact of cell cycle noise on gene circuit dynamics. For bistable genetic switches and excitable circuits, we find that transitions between metastable states most likely occur just after cell division and that this concentration effect intensifies in the presence of transcriptional delay. We explain this concentration effect with a three-states stochastic model. For genetic oscillators, we quantify the temporal correlations between daughter cells induced by cell division. Temporal correlations must be captured properly in order to accurately quantify noise sources within gene networks.