Phage anti-CRISPR control by an RNA- and DNA-binding helix-turn-helix protein.

In all organisms, regulation of gene expression must be adjusted to meet cellular requirements and frequently involves helix-turn-helix (HTH) domain proteins1. For instance, in the arms race between bacteria and bacteriophages, rapid expression of phage anti-CRISPR (acr) genes upon infection enables evasion from CRISPR-Cas defence; transcription is then repressed by an HTH-domain-containing anti-CRISPR-associated (Aca) protein, probably to reduce fitness costs from excessive expression2-5. However, how a single HTH regulator adjusts anti-CRISPR production to cope with increasing phage genome copies and accumulating acr mRNA is unknown. Here we show that the HTH domain of the regulator Aca2, in addition to repressing Acr synthesis transcriptionally through DNA binding, inhibits translation of mRNAs by binding conserved RNA stem-loops and blocking ribosome access. The cryo-electron microscopy structure of the approximately 40 kDa Aca2-RNA complex demonstrates how the versatile HTH domain specifically discriminates RNA from DNA binding sites. These combined regulatory modes are widespread in the Aca2 family and facilitate CRISPR-Cas inhibition in the face of rapid phage DNA replication without toxic acr overexpression. Given the ubiquity of HTH-domain-containing proteins, it is anticipated that many more of them elicit regulatory control by dual DNA and RNA binding.

Computational characterization of recombinase circuits for periodic behaviors.

Recombinases are site-specific proteins found in nature that are capable of rearranging DNA. This function has made them promising gene editing tools in synthetic biology, as well as key elements in complex artificial gene circuits implementing Boolean logic. However, since DNA rearrangement is irreversible, it is still unclear how to use recombinases to build dynamic circuits like oscillators. In addition, this goal is challenging because a few molecules of recombinase are enough for promoter inversion, generating inherent stochasticity at low copy number. Here, we propose six different circuit designs for recombinase-based oscillators operating at a single copy number. We model them in a stochastic setting, leveraging the Gillespie algorithm for extensive simulations, and show that they can yield coherent periodic behaviors. Our results support the experimental realization of recombinase-based oscillators and, more generally, the use of recombinases to generate dynamic behaviors in synthetic biology.

RNA Compensation: A Positive Feedback Insulation Strategy for RNA-Based Transcription Networks.

The lack of signaling modularity of biomolecular systems poses major challenges toward engineering complex networks. Directional signaling between an upstream and a downstream circuit requires the presence of binding events, which result in the consumption of regulatory molecules and can compromise the operation of the upstream circuit. This issue has been previously addressed by introducing insulation strategies that include high-gain negative feedback and activation-deactivation reaction cycles. In this paper, we focus on RNA-based circuits and propose a new positive-feedback strategy to mitigate signal consumption that we propose occurs for each regulatory event due to irreversible binding of the RNA input to the RNA target. To mitigate this, an extra RNA input is added in tandem with transcription output to compensate the RNA consumption, leading to concentration robustness of the input RNA molecule regardless of the amount of downstream modules. We term this strategy RNA compensation, and it can be applied to systems that have a stringent input-output gain, such as Small Transcription Activating RNAs (STARs). Our theoretical analysis shows that RNA compensation not only eliminates the signaling consumption in individual STAR-based regulators, but also improves the composability of STAR cascades and the modularity of RNA bistable systems.

Ultrasensitive molecular controllers for quasi-integral feedback.

Feedback control has enabled the success of automated technologies by mitigating the effects of variability, unknown disturbances, and noise. While it is known that biological feedback loops reduce the impact of noise and help shape kinetic responses, many questions remain about how to design molecular integral controllers. Here, we propose a modular strategy to build molecular quasi-integral feedback controllers, which involves following two design principles. The first principle is to utilize an ultrasensitive response, which determines the gain of the controller and influences the steady-state error. The second is to use a tunable threshold of the ultrasensitive response, which determines the equilibrium point of the system. We describe a reaction network, named brink controller, that satisfies these conditions by combining molecular sequestration and an activation/deactivation cycle. With computational models, we examine potential biological implementations of brink controllers, and we illustrate different example applications.

Homogeneous Time Constants Promote Oscillations in Negative Feedback Loops.

Biological oscillators are present in nearly all self-regulating systems, from individual cells to entire organisms. In any oscillator structure, a negative feedback loop is necessary, but not sufficient to guarantee the emergence of periodic behaviors. The likelihood of oscillations can be improved by careful tuning of the system time constants and by increasing the loop gain, yet it is unclear whether there is any general relationship between optimal time constants and loop gain. This issue is particularly relevant in genetic oscillators resulting from a chain of different subsequent biochemical events, each with distinct (and uncertain) kinetics. Using two families of genetic oscillators as model examples, we show that the loop gain required for oscillations is minimum when all elements in the loop have the same time constant. On the contrary, we show that homeostasis is ensured if a single element is considerably slower than the others.

A Robust Molecular Network Motif for Period-Doubling Devices.

Life is sustained by a variety of cyclic processes such as cell division, muscle contraction, and neuron firing. The periodic signals powering these processes often direct a variety of other downstream systems, which operate at different time scales and must have the capacity to divide or multiply the period of the master clock. Period modulation is also an important challenge in synthetic molecular systems, where slow and fast components may have to be coordinated simultaneously by a single oscillator whose frequency is often difficult to tune. Circuits that can multiply the period of a clock signal (frequency dividers), such as binary counters and flip-flops, are commonly encountered in electronic systems, but design principles to obtain similar devices in biological systems are still unclear. We take inspiration from the architecture of electronic flip-flops, and we propose to build biomolecular period-doubling networks by combining a bistable switch with negative feedback modules that preprocess the circuit inputs. We identify a network motif and we show it can be "realized" using different biomolecular components; two of the realizations we propose rely on transcriptional gene networks and one on nucleic acid strand displacement systems. We examine the capacity of each realization to perform period-doubling by studying how bistability of the motif is affected by the presence of the input; for this purpose, we employ mathematical tools from algebraic geometry that provide us with valuable insights on the input/output behavior as a function of the realization parameters. We show that transcriptional network realizations operate correctly also in a stochastic regime when processing oscillations from the repressilator, a canonical synthetic in vivo oscillator. Finally, we compare the performance of different realizations in a range of realistic parameters via numerical sensitivity analysis of the period-doubling region, computed with respect to the input period and amplitude. Our mathematical and computational analysis suggests that the motif we propose is generally robust with respect to specific implementation details: functionally equivalent circuits can be built as long as the species-interaction topology is respected. This indicates that experimental construction of the circuit is possible with a variety of components within the rapidly expanding libraries available in synthetic biology.

Dynamic Control of Aptamer-Ligand Activity Using Strand Displacement Reactions.

Nucleic acid aptamers are an expandable toolkit of sensors and regulators. To employ aptamer regulators within nonequilibrium molecular networks, the aptamer-ligand interactions should be tunable over time, so that functions within a given system can be activated or suppressed on demand. This is accomplished through complementary sequences to aptamers, which achieve programmable aptamer-ligand dissociation by displacing the aptamer from the ligand. We demonstrate the effectiveness of our simple approach on light-up aptamers as well as on aptamers inhibiting viral RNA polymerases, dynamically controlling the functionality of the aptamer-ligand complex. Mathematical models allow us to obtain estimates for the aptamer displacement kinetics. Our results suggest that aptamers, paired with their complement, could be used to build dynamic nucleic acid networks with direct control over a variety of aptamer-controllable enzymes and their downstream pathways.

Stability analysis of an artificial biomolecular oscillator with non-cooperative regulatory interactions.

Oscillators are essential to fuel autonomous behaviours in molecular systems. Artificial oscillators built with programmable biological molecules such as DNA and RNA are generally easy to build and tune, and can serve as timers for biological computation and regulation. We describe a new artificial nucleic acid biochemical reaction network, and we demonstrate its capacity to exhibit oscillatory solutions. This network can be built in vitro using nucleic acids and three bacteriophage enzymes, and has the potential to be implemented in cells. Numerical simulations suggest that oscillations occur in a realistic range of reaction rates and concentrations.

Molecular Titration Promotes Oscillations and Bistability in Minimal Network Models with Monomeric Regulators.

Molecular titration is emerging as an important biochemical interaction mechanism within synthetic devices built with nucleic acids and the CRISPR/Cas system. We show that molecular titration in the context of feedback circuits is a suitable mechanism to enhance the emergence of oscillations and bistable behaviors. We consider biomolecular modules that can be inhibited or activated by input monomeric regulators; the regulators compete with constitutive titrating species to determine the activity of their target. By tuning the titration rate and the concentration of titrating species, it is possible to modulate the delay and convergence speed of the transient response, and the steepness and dead zone of the stationary response of the modules. These phenomena favor the occurrence of oscillations when modules are interconnected to create a negative feedback loop; bistability is favored in a positive feedback interconnection. Numerical simulations are supported by mathematical analysis showing that the capacity of the closed loop systems to exhibit oscillations or bistability is structural.

Computing the structural influence matrix for biological systems.

We consider the problem of identifying structural influences of external inputs on steady-state outputs in a biological network model. We speak of a structural influence if, upon a perturbation due to a constant input, the ensuing variation of the steady-state output value has the same sign as the input (positive influence), the opposite sign (negative influence), or is zero (perfect adaptation), for any feasible choice of the model parameters. All these signs and zeros can constitute a structural influence matrix, whose (i, j) entry indicates the sign of steady-state influence of the jth system variable on the ith variable (the output caused by an external persistent input applied to the jth variable). Each entry is structurally determinate if the sign does not depend on the choice of the parameters, but is indeterminate otherwise. In principle, determining the influence matrix requires exhaustive testing of the system steady-state behaviour in the widest range of parameter values. Here we show that, in a broad class of biological networks, the influence matrix can be evaluated with an algorithm that tests the system steady-state behaviour only at a finite number of points. This algorithm also allows us to assess the structural effect of any perturbation, such as variations of relevant parameters. Our method is applied to nontrivial models of biochemical reaction networks and population dynamics drawn from the literature, providing a parameter-free insight into the system dynamics.