William Ott

Engineered temperature compensation in a synthetic genetic clock

Significance Synthetic gene circuits are often fragile, as perturbations to cellular conditions frequently alter their behavior. This lack of robustness limits the utility of engineered gene circuits and hinders advances in synthetic biology. Here, we demonstrate that environmental sensitivity can be reduced by simultaneously engineering circuits at the protein and network levels. Specifically, we designed and constructed a synthetic genetic clock that exhibits temperature compensation—the clock’s period does not depend on temperature. This feature is nontrivial since biochemical reactions speed up with increasing temperature. To accomplish this goal, we engineered thermal-inducibility into the clock’s regulatory structure. Computational modeling predicted and experiments confirmed that this thermal-inducibility results in a clock with a stable period across a large range of temperatures. Synthetic biology promises to revolutionize biotechnology by providing the means to reengineer and reprogram cellular regulatory mechanisms. However, synthetic gene circuits are often unreliable, as changes to environmental conditions can fundamentally alter a circuit’s behavior. One way to improve robustness is to use intrinsic properties of transcription factors within the circuit to buffer against intra- and extracellular variability. Here, we describe the design and construction of a synthetic gene oscillator in Escherichia coli that maintains a constant period over a range of temperatures. We started with a previously described synthetic dual-feedback oscillator with a temperature-dependent period. Computational modeling predicted and subsequent experiments confirmed that a single amino acid mutation to the core transcriptional repressor of the circuit results in temperature compensation. Specifically, we used a temperature-sensitive lactose repressor mutant that loses the ability to repress its target promoter at high temperatures. In the oscillator, this thermoinduction of the repressor leads to an increase in period at high temperatures that compensates for the decrease in period due to Arrhenius scaling of the reaction rates. The result is a transcriptional oscillator with a nearly constant period of 48 min for temperatures ranging from 30 °C to 41 °C. In contrast, in the absence of the mutation the period of the oscillator drops from 60 to 30 min over the same temperature range. This work demonstrates that synthetic gene circuits can be engineered to be robust to extracellular conditions through protein-level modifications.

Stochastic Delay Accelerates Signaling in Gene Networks

The creation of protein from DNA is a dynamic process consisting of numerous reactions, such as transcription, translation and protein folding. Each of these reactions is further comprised of hundreds or thousands of sub-steps that must be completed before a protein is fully mature. Consequently, the time it takes to create a single protein depends on the number of steps in the reaction chain and the nature of each step. One way to account for these reactions in models of gene regulatory networks is to incorporate dynamical delay. However, the stochastic nature of the reactions necessary to produce protein leads to a waiting time that is randomly distributed. Here, we use queueing theory to examine the effects of such distributed delay on the propagation of information through transcriptionally regulated genetic networks. In an analytically tractable model we find that increasing the randomness in protein production delay can increase signaling speed in transcriptional networks. The effect is confirmed in stochastic simulations, and we demonstrate its impact in several common transcriptional motifs. In particular, we show that in feedforward loops signaling time and magnitude are significantly affected by distributed delay. In addition, delay has previously been shown to cause stable oscillations in circuits with negative feedback. We show that the period and the amplitude of the oscillations monotonically decrease as the variability of the delay time increases.

Transcriptional Delay Stabilizes Bistable Gene Networks

Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay dramatically increases the mean residence times near stable states. To explain this, we introduce a non-Markovian, analytically tractable reduced model. The model shows that stabilization is the consequence of an increased number of failed transitions between stable states. Each of the bistable systems that we simulate behaves in this manner.

From Limit Cycles to Strange Attractors

We define a quantitative notion of shear for limit cycles of flows. We prove that strange attractors and SRB measures emerge when systems exhibiting limit cycles with sufficient shear are subjected to periodic pulsatile drives. The strange attractors possess a number of precisely-defined dynamical properties that together imply chaos that is both sustained in time and physically observable.

Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.

A Borel–Cantelli lemma for nonuniformly expanding dynamical systems

Let be a sequence of sets in a probability space such that . The classical Borel–Cantelli (BC) lemma states that if the sets An are independent, then μ({x X : x An for infinitely many values of n}) = 1. We present analogous dynamical BC lemmas for certain sequences of sets (An) in X (including nested balls) for a class of deterministic dynamical systems T : X → X with invariant probability measures. Our results apply to a class of Gibbs–Markov maps and one-dimensional nonuniformly expanding systems modelled by Young towers. We discuss some applications of our results to the extreme value theory of deterministic dynamical systems.

Strange Attractors in Periodically-Kicked Degenerate Hopf Bifurcations

We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of periodically-kicked degenerate supercritical Hopf bifurcations. The results and their proofs make use of a k-parameter version of the theory of rank one maps.

Tuning the dynamic range of bacterial promoters regulated by ligand-inducible transcription factors

One challenge for synthetic biologists is the predictable tuning of genetic circuit regulatory components to elicit desired outputs. Gene expression driven by ligand-inducible transcription factor systems must exhibit the correct ON and OFF characteristics: appropriate activation and leakiness in the presence and absence of inducer, respectively. However, the dynamic range of a promoter (i.e., absolute difference between ON and OFF states) is difficult to control. We report a method that tunes the dynamic range of ligand-inducible promoters to achieve desired ON and OFF characteristics. We build combinatorial sets of AraC-and LasR-regulated promoters containing −10 and −35 sites from synthetic and Escherichia coli promoters. Four sequence combinations with diverse dynamic ranges were chosen to build multi-input transcriptional logic gates regulated by two and three ligand-inducible transcription factors (LacI, TetR, AraC, XylS, RhlR, LasR, and LuxR). This work enables predictable control over the dynamic range of regulatory components.For synthetic gene circuits to behave as designed, ligand-inducible promoters should display predictable ON/OFF characteristics. Here the authors design multi-input hybrid promoters to build transcriptional logic gates.

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.

Recurrence in pairs

We introduce and study the notion of weak product recurrence. Two sufficient conditions for this type of recurrence are established. We deduce that any point with a dense orbit in either the full one-sided shift on a finite number of symbols or a mixing subshift of finite type is weakly product recurrent. This observation implies that distality does not follow from weak product recurrence. We have therefore answered, in the negative, a question posed by Auslander and Furstenberg.